Loading...

Meaning of the Equal Sign
Quiz by allison
Customize this quiz to suit your class
Instantly translate to 100+ languages
Tag the questions with any skills you have. Your dashboard will track each student's mastery of each skill.
Give this quiz to my class
GUIDELINES ON THE ESTABLISHMENT AND IMPLEMENTATION OF THE RESULTS-BASED PERFORMANCE MANAGEMENT SYSTEM IN THE DEPARTMENT OF EDUCATION I. Rationale 1. The Civil Service Commission (CSC), through the issuance of Memorandum Circular (MC) No. 06, series of 2012, sets the guidelines on the establishment and implementation of the Strategic Performance Management System (SPMS) in all government agencies. The SPMS gives emphasis to the strategic alignment of the agency’s thrusts with the day-to-day operation of the units and individual personnel within the organization. It focuses on measures of performance vis-a-vis the targeted milestones, and provides a credible and verifiable basis for assessing the organizational outcomes and the collective performance of the government employees. 2. As a learner-centered institution, the Department of Education (DepEd) is committed to continuously improve itself to better serve the Filipino learners and the community. The adoption of the SPMS in DepEd strengthens the culture of performance and accountability in the agency, with the DepEd’s mandate, vision and mission at its core. 3. There is a need to concretize the linkage between the organizational thrusts and the performance management system. It is important to ensure organizational effectiveness and track individual improvement and efficiency by cascading the institutional accountabilities to the various levels, units and individual personnel, as anchored on the establishment of a rational and factual basis for performance targets and measures. Finally, it is necessary to link the SPMS with other systems relating to human resources and to ensure adherence to the principle of performance-based tenure and incentives. 4. In view of the above, this Order aims to adopt the SPMS as the Results-based Performance Management System (RPMS). II. Scope of Policy 5. This DepEd Order provides for the establishment and implementation of the RPMS in all DepEd schools and offices, covering all officials and employees, school-based and non school-based, in the Department holding regular plantilla positions. It stipulates the specific mechanisms, criteria and processes for the performance target setting, monitoring, evaluation and development planning. IV. Policy Statement 9. The DepEd hereby sets the guidelines on the establishment and implementation of the Results-based Performance Management System (RPMS) in the Department, stipulating the strategies, methods, tools and rewards for assessing the accomplishments vis-a-vis the commitments. This will be used for measuring and rewarding higher levels of performance of the various units and development planning of all personnel in all levels. 10. For non school-based personnel, the RPMS shall provide for an objective and verifiable basis for rating and ranking the performance of units and individual personnel in view of the granting of the Performance-Based Bonus (PBB) starting 2015. 11. For school-based personnel, the RPMS shall be used only as an appraisal tool, which shall be the basis for training and development. The granting of PBB shall be governed by the existing PBB guidelines. 12. The Department shall adopt the RPMS framework shown in Annex B. 13. The DepEd RPMS shall follow the four-stage performance management system cycle as prescribed by the CSC: i. Performance planning and commitment (Phase I); ii. Performance monitoring and coaching (Phase II); iii. Performance review and evaluation (Phase III); and iv. Performance rewarding and development planning (Phase IV). V. Performance Cycle/Process 14. The RPMS shall align the performance targets and accomplishments with the Department’s mandate, vision, mission and strategic goals. It shall ensure 100% results orientation vis-a-vis the planned targets. On the other hand, the ratee’s demonstration of the required competencies shall be monitored for developmental purposes only. 15. The RPMS cycle shall cover performance for one whole year. All school-based personnel shall follow a performance cycle starting in April of the current year and ending in March of the following year; while non school-based personnel shall follow a performance cycle starting in January and ending in December. Annexes C and D illustrate the performance cycles which shall apply to school-based and non school-based personnel, respectively. 16. The performance planning and commitment shall be done prior to the beginning of the performance cycle; while the performance monitoring and coaching shall take place immediately after Phase I, and continue throughout the performance cycle. The performance review and evaluation, as well as the performance rewarding and development planning shall be done at the end of the performance cycle. A. Phase I: Performance Planning and Commitment 17. The performance planning and commitment shall be done prior to the start of the performance cycle where the rater meets with the ratee to discuss and agree on the following: i. Office KRAs, Objectives and Performance Indicators as anchored to the overall organizational outcomes; and ii. Individual KRAs, Objectives and Performance Indicators as anchored to the Office KRAs and Objectives. 18. The Office Performance Commitment and Review Form (OPCRF) shall be accomplished by the head of office to reflect the Office KRAs, Objectives and Performance Indicators. The head of office, in coordination with the Planning Office, shall ensure alignment of the office plans and commitments to the overall organizational outcomes. The OPCRF shall be equivalent to the IPCRF of the head of office. A sample of the filled out OPCRF, including the instructions for accomplishing the form, is shown in Annex E. 19. The Individual Performance Commitment and Review Form (IPCRF) shall be accomplished by the individual personnel to reflect the agreed Individual KRAs, Objectives and Performance Indicators. A sample of the filled out IPCRF, including the instructions for accomplishing the form, is shown in Annex F. 20. Defining the Key Result Areas. The head of office, in coordination with the Planning Office, shall define the office KRAs as anchored on the overall organizational outcomes. The rater and the ratee shall discuss and agree on the break down of the office KRAs into individual KRAs. Three (3) to five (5) KRAs shall be defined for each office and individual employee. KRAs are broad categories of general outputs or outcomes. It is the mandate or function of the office and/or individual employee. The KRA is the reason why an office and/or job exist. It is an area where the office and/or individual employee are expected to focus on. 21. Setting the Objectives. The head of office shall set three (3) objectives per office KRA. The rater and the ratee shall discuss and agree on three (3) objectives per individual KRA. Objectives are specific tasks, which an office and/or employee need to do to achieve their specific KRAs. In objective setting, the SMART criteria, which stands for Specific, Measurable, Attainable, Relevant, Time Bound, shall be applied. The SMART criteria are illustrated in Annex G. 22. Setting the Timeline. The timeline shall define the target date for accomplishing each of the Objectives. The timeline for the office Objectives shall be set by the head of office in coordination with the Planning Office and School Planning Team; while the timeline for the individual Objectives shall be discussed and agreed by the rater and the ratee. 23. Assigning the Weight. Assigning of weights shall be done per KRA. Weights for each office KRA shall be assigned by the head of office in coordination with the Planning Office; while the weights for each of the individual KRAs shall be discussed and agreed upon by the rater and the ratee. 24. Identifying the Performance Indicators. Using a five (5)-point rating scale, the head of office shall identify a performance indicator for each of the office objectives, while the rater and the ratee shall identify and agree on the performance indicator for each of the individual objectives. Performance indicators are exact quantification of objectives expressed through rubrics. They are assessment tools, which gauge whether a performance is positive or negative. In identifying the performance indicator, the operational definition or meaning of each numerical rating shall be indicated under each relevant dimension (i.e., quality, efficiency, or timeliness) per performance target or success indicator. This shall ensure that the rating is objective, impartial and verifiable. Table 1 below discusses the performance measures by which the indicator must satisfy. Table 1. Performance Measures CATEGORY DEFINITION Effectiveness/Quality The extent to which actual performance compares with targeted performance. The degree to which objectives are achieved and the extent to which targeted problems are solved. In management, effectiveness relates to getting the right things done. Efficiency The extent to which time or resources is used for the intended task or purpose. Measures whether targets are accomplished with a minimum amount or quantity of waste, expense, or unnecessary effort. Timeliness Measures whether the deliverable was done on time based on the requirements of the rules and regulations, and/or clients/stakeholders. Time-related performance indicators evaluate such things as project completion deadlines, time management skills and other time-sensitive expectations. Some Performances are only rated on quality and efficiency, some on quality and timeliness, and others on efficiency only. You need not use all three (3) categories. 25. Demonstration of Competencies. During Phase I, the rater shall discuss with the ratee the competencies required of the individual personnel. Competencies are defined as the knowledge, skills and behavior that individuals demonstrate in achieving one’s results. Competencies shall uphold the DepEd’s core values. They represent the way individuals define and live the values. 26. DepEd shall adopt four classes of competencies as follows: i. Core behavioral competencies are competencies, which cut across the organization; ii. Leadership competencies are competencies intended for managerial positions; a. Third level officials b. Chiefs and Assistant Chiefs c. School Heads and Department Heads iii. Staff Core Skills are competencies intended for staff and teaching-related personnel; and iv. Teaching competencies are competencies intended for teachers. The DepEd-required competencies are illustrated in Annex I. 27. The ratee’s demonstration of the required competencies shall be monitored to effectively plan the interventions needed for behavioral and professional development. The assessment in the demonstration of competencies shall not be reflected in the final rating. 28. Reaching Agreement. Once the office and individual KRAs, Objectives and Performance Indicators are clearly defined, the rater and the ratee shall commit and reach an agreement by signing the OPCRF and IPCRF. The signed/approved OPCRF and IPCRF shall be the basis for monitoring and assessment, which shall take place in Phases II and III, respectively. B. Phase II: Performance Monitoring and Coaching 29. The performance monitoring and coaching shall commence after the rater and the ratee commit on the KRAs, Objectives and Performance Indicators, and sign the OPCRF and IPCRF. This shall be done throughout the year. 30. The two (2) main components of Phase II are the following: i. Performance monitoring; and ii. Coaching and feedback. 31. Performance monitoring shall provide key inputs and objective basis for rating. It shall facilitate feedback and provide evidence of performance. Performance monitoring shall be the responsibility of both the rater and the ratee who agree to track and record significant incidents through the use of the Performance Monitoring and Coaching Form (PMCF) shown in Annex J. Significant incidents are actual events and behaviors in which both positive and negative performances are observed and documented. 32. Coaching and feedback shall be a continuous process. Coaching and feedback shall be provided by the rater and/or shall be sought by the ratee to improve work performance and behavior. The rater, as the coach or mentor of the ratee, playing a critical role in the performance monitoring and coaching, shall provide an enabling environment and intervention to improve the office performance and to manage and develop individual potentials. 33. The PMCF shall capture the significant incidents. It shall provide a record of demonstrated behaviors, competencies and performance, and shall be an effective substitute in the absence of quantifiable data. The rater and the ratee shall sign each significant incident recorded in the PMCF to ensure that agreement has been reached. C. Phase III: Performance Review and Evaluation 34. The performance review and evaluation shall be done at the end of the performance cycle to assess the office and individual employee’s performance level based on the commitments and measures as contained in the signed OPCRF and IPCRF. 35. A mid-year review is prescribed to determine the progress in achieving the Objectives. In exceptional cases, and only if the situation warrants, a one-time recalibration of office and individual Objectives shall be allowed during the mid-year review. Exceptional cases shall include instances when high level decisions are taken into effect such as changes in strategic directions, and circumstances beyond the control of the ratee such as natural and/or man-made calamities, including typhoon, earthquake and other fortuitous events. During the mid-year review, the rater shall inform in writing the ratee of the status of performance, in case of an Unsatisfactory or Poor performance. Coaching, feedback and appropriate interventions shall be provided where necessary. 36. The RPMS shall put premium on KRAs towards the realization of organizational vision, mission, strategic priorities and the OPIF logframe. Hence, rating for planned and/or intervening tasks shall always be supported by reports, documents or any output as proofs of actual performance. In the absence of said bases or proofs, a particular task shall not be rated and shall be disregarded. 37. Office and Individual Performance Assessment. The head of office, in coordination with the Planning Office, shall assess the performance of the office vis-a-vis the committed targets at the beginning of the performance cycle. The rater and the ratee shall discuss and agree on the individual assessment based on the actual accomplishments of each of the KRAs and Objectives. The final rating shall be based solely on the accomplishment of the specific objectives as measured by the Performance Indicators. The OPCRF and IPCRF shall be accomplished and completed by the rater and the ratee to: i. Reflect actual accomplishments and results; ii. Rate each of the objectives; iii. Compute for the score per objective; iv. Determine the overall rating for accomplishments; v. Reach an agreement; and vi. Assess the competencies. 38. Initial self-rating shall be encouraged prior to the rater-ratee discussion. 39. Third Level Officials, as heads of offices, shall accomplish the OPCRF for submission to the Planning Office. The individual assessment of Third Level Officials shall be contained in the CESPES Forms for submission to the Career Executive Service Board (CESB). The BHROD and Personnel Division shall be furnished a copy of both forms. 40. Actual Results. The rater and the ratee shall discuss and agree on the actual accomplishments and results based on the performance commitments and measures made at the beginning of the rating period. They shall evaluate each objective whether it has been achieved or not. The significant incidents as reflected in the PMCF shall be considered for the actual results. 41. Rating the Objectives. Based on the actual accomplishments and results, each of the Objectives shall be rated using the rating scale specified below: Table 2. The RPMS Rating Scale NUMERICAL RATING ADJECTIVAL RATING DESCRIPTION OF MEANING OF RATING 5 Outstanding Performance represents an extraordinary level of achievement and commitment in terms of quality and time, technical skills and knowledge, ingenuity, creativity and initiative. Employees at this performance level should have demonstrated exceptional job mastery in all major areas of responsibility. Employee achievement and contributions to the organization are of marked excellence. 4 Very Satisfactory Performance exceeded expectations. All goals, objectives and targets were achieved above the established standards. 3 Satisfactory Performance met expectations in terms of quality of work, efficiency and timeliness. The most critical annual goals were met. 2 Unsatisfactory Performance failed to meet expectations, and/or one or more of the most critical goals were not met. 1 Poor Performance was consistently below expectations, and/or reasonable progress toward critical goals was not made. Significant improvement is needed in one or more important areas. The final assessment shall correspond to the adjectival description of Outstanding, Very Satisfactory, Satisfactory, Unsatisfactory or Poor. The range of adjectival rating is as per attached in Forms A, B, and C. 42. Process for Computing the Score per KRA. i. The rater and ratee shall ensure that each KRA has been assigned weight according to priority. ii. As an option, the rater and ratee may assign weights to objectives which shall be equal to the total weight assigned to a particular KRA. KRA 1 – Weight assigned is 40% Objective 1 is 20% Objective 2 is 10% Objective 3 is 10% iii. The score per KRA shall be computed using the following formula: 43. Plus Factor. The plus factor shall be considered as another KRA. These are value adding accomplishments, which are not covered within the regular duties and responsibilities. The weight on the plus factor shall not exceed the weight of the highest mandated KRA. For teachers, the plus factor shall be limited to work/activities, which contribute to the teaching-learning process. 44. Determining the Overall Rating for Accomplishments. The overall rating/assessment for the accomplishments shall fall within the following adjectival ratings and shall be in three (3) decimal points: Table 3. Adjectival Ratings RANGE ADJECTIVAL RATING 4.500-5.000 Outstanding 3.500-4.499 Very Satisfactory 2.500-3.499 Satisfactory 1.500-2.499 Unsatisfactory below 1.499 Poor 45. Reaching Agreement. Upon determining the overall rating for the actual accomplishments and results, the rater and the ratee shall reach an agreement by signing the OPCRF and IPCRF. The average rating of individual staff members should not go higher than the collective performance assessment of the office. 46. Assessing the Competencies. The rater shall discuss with the ratee the set of competencies observed during the performance cycle. The competencies shall not be reflected in the final rating. Competencies shall be monitored for developmental purposes. In evaluating the individual’s demonstration of competencies, the rating scale in Table 4 shall apply: Table 4. The DepEd Competencies Scale SCALE DEFINITION 5 Role model 4 Consistently demonstrates 3 Most of the time demonstrates 2 Sometimes demonstrates 1 Rarely demonstrates 5 (role model) – all competency indicators 4 (consistently demonstrates) – four competency indicators 3 (most of the time demonstrates) – three competency indicators 2 (sometimes demonstrates) – two competency indicators 1 (rarely demonstrates) – one competency indicator D. Phase IV: Performance Rewarding and Development Planning 47. The results of the performance review and evaluation shall be used in performance rewarding and development planning. This phase shall be done after Phase III. 48. The rater shall discuss and provide qualitative comments, observations and recommendations in the individual employee’s performance commitment, competency assessment and significant incidents which shall be used for training and professional development. These can be written under the strengths and development needs column of the Part IV-Development Plans of the IPCRF. 49. The rater and the ratee shall identify and discuss the individual’s strengths and development needs, and reflect them in the Part IV-Development Plans of the IPCRF. The competencies which the ratee demonstrated consistently and the areas, where the ratee meet or exceed expectations shall be referred to as the ratee’s strengths. The competencies, which the ratee rarely demonstrates and the areas where the ratee has room for improvement and has not met the expectations, shall be identified as the ratee’s development needs. Make a situational SOLO-based questions in the context of school leadership
1.Linguistics is the science that studies language. 2.Linguist:Someone who studies linguistics. 3.The Subfields of Linguistics Phonetics deals with the sounds of language. Phonology deals with how the sounds are organized. Morphology deals with how sounds are put together to form words. Syntax deals with how sentences are formed. Semantics deals with the meaning of words, sentences, and texts. Pragmatics deals with how sentences and texts are used in the world (i.e., in context) Text Linguistics deals with units larger than sentences, such as paragraphs and texts. 4.Prescriptive: This approach consists basically of stating what is considered right and wrong in language. 5.Descriptive: This approach, on the other hand, consists of describing the facts. Descriptive linguistics is dedicated to describing the rules of the language, and the language is seen as essentially rule governed. 6.Language is rule-governed, creative, universal, innate, and learned, all at the same time. 7.Linguists understand language as a system of arbitrary vocal signs. 8.Linguistic signs: involve sequences of sounds which represent concrete objects and events as well as abstractions.Signs may be related to the things they represent in a number of ways. 9.Iconic: which resemble the things they represent (as do, for example, photographs, diagrams, star charts, or chemical models). 10.Indexical: which point to or have a necessary connection with the things they represent (as do, for example, smoke to fire, a weathercock to the direction of the wind, a symptom to an illness, a smile to happiness, or a frown to anger). 11.Describe the characteristics of human language: Creative: (The structural elements of human language can be combined to produce new utterances, which neither the speaker nor his hearers may ever have made or heard before.) Rule-governed: (Language is made of rules.) Universal: (There are some aspects that are present in all languages of the world.) Innate:(all humans possess an innate capacity for language, activated in infancy by minimal environmental stimuli. Chomsky) Uniquely human: (Language is what sets us apart from other species. It is what makes us human.) Learned:(Children acquire language from their natural setting.) 12.Differentiate between iconic, indexical and symbolic signs. A. iconic, which resemble the things they represent (as do, for example, photographs, diagrams, star charts, or chemical models) B. indexical, which point to or have a necessary connection with the things they represent (as do, for example, smoke to fire, a weathercock to the direction of the wind, a symptom to an illness, a smile to happiness, or a frown to anger). c. symbolic, which are only conventionally related to the thing they represent (as do, for example, a flag to a nation, a rose to love, a wedding ring to marriage). 12. Distinguish between different senses of the grammar word. The prescriptivist´s grammar (Grammar is a set of rules that label the different utterances as either right or wrong.) The descriptivist´s grammar (Grammar is a set of rules that govern the langauge spoken by people. ) The linguist´s grammar (Grammar is the subconscious knowledge of the set of rules that enables speakers to use the language) The speaker´s grammar (Grammar is the intrinsic linguistic knowledge within a native speaker) 13.Describe common fallacies about language and grammar: ►One type of grammar is simpler than another. ►Changes in grammar involve deterioration in a language ►Grammars should be logical and analogical (that is, regular) ►People must be taught the grammatical rules of their language. ►Only some languages have grammar. ►Grammars differ from each other in unpredictable ways. 14.Generality: All Languages Have a Grammar 15. Equality: All Grammars Are Equal 16.Changeability: Grammars Change Over Time 17. Universality: Grammars Are Alike in Basic Ways 18.Tacitness: Grammatical Knowledge Is Subconscious 19.Linguistics is defined as the study of language systems. It is the scientific study of language. 20.Historical approach:It is the study of language change. 21.Linguistic Competence: is the unconscious knowledge speakers of a language have about the system that enables them to create and understand novel utterances. 22.Performance: is the use of it. Performance is “the actual use of language in concrete situations.” 23.I-Language (internal language): which is the intrinsic linguistic knowledge within a native speaker. 24.E-Language (external language): which is the observable language—the output from a speaker. 25.Parole ('speech') refers to the concrete instances of the use of langue, including texts which provide the ordinary research material for linguistics. 26.Langue: 27.Language: is a system of communication that is non-stereotyped and non-finite; it is unlimited in its scope. 28.Grammar: to refer to a subconscious linguistic system of a particular type. Grammar makes possible the production and comprehension of a potentially unlimited number of utterances. 29.Communication and animals: Selecting a mode of communication (speech,writing, gesture). Delivering the symbols through a medium, a physical basis for communication, light, air, or ink. Decoding of the symbols to obtain the information. 30.SIGNS: Communication relies on using something to stand for something else. Words are an obvious example of this: You do not have to have a car, a sandwich, or your cousin present in order to talk about them—the words car, sandwich, and cousin stand for them instead. This same phenomenon is found in animal communication as well. 31.The signifier: A signifier is that part of a sign that stimulates at least one sense organ of the receiver of a message.A signifier can also be a picture, a photograph, a sign language gesture, or one of the many other words for tree in different languages. 32.The signified: The signified component of the sign refers to both the real world object it represents and its conceptual content. The first of these is the real world content of the sign, its extension or referent within a system of signs such as English, avian communication, or sign language. 33.Iconic signs or icons: always bear some resemblance to their referent. A photograph is an iconic sign; so too is a stylized silhouette of a female or a male on a restroom door. 34.Some iconic tokens: a. open-mouth threat by a Japanese macaque; b. park recreation signs; c. onomatopoeic words in English. 35.An indexical sign, or index, fulfils its function by pointing out its referent, typically by being a partial or representative sample of it. Indexes are not arbitrary, since their presence has in some sense been caused by their referent. For this reason it is sometimes said that there is a causal link between an indexical sign and its referent.The track of an animal, for example, points to the existence of the animal by representing a part of it. The presence of smoke is an index of fire. 36.Symbolic signs: bear an arbitrary relationship to their referents and in this way are distinct from both icons and indexes. Human language is highly symbolic in that the vast majority of its signs bear no inherent resemblance or causal connection to their referents, as the following words show. 37.Mixed signs Signs: are not always exclusively of one type or another. Symptomatic signs, for example, may have iconic properties, as when a dog opens its mouth in a threat to bite. Symbolic signs such as traffic lights are symptomatic in that they reflect the internal state of the mechanism that causes them to change color. 38.Signals: All signs can act as signals when they trigger a specific action on the part of the receiver, as do traffic lights, words in human language such as the race starter's "Go!", or the warning calls of birds. 39.SIGN STRUCTURE: No matter what their type, signs show different kinds of structure. A basic distinction is made between graded and discrete sign structure. 40.Graded signs convey their meaning by changes in degree. A good example of a gradation in communication is voice volume. The more you want to be heard, the louder you speak along an increasing scale of loudness. There are no steps or jumps from one level to the next that can be associated with a specific change in meaning. 41.Discrete signs are distinguished from each other by categorical (stepwise) differences. There is no gradual transition from one sign to the next. The words of human language are good examples of discrete signs. 42.A VIEW OF ANIMAL COMMUNICATION ►Largely iconic ►Largely symptomatic ►Little arbitrary ►Not deliberate ►Not conscious ►Not symbolic ►Stimulus bound
Introduction to Free Fall A free-falling object is an object that is falling under the sole influence of gravity. Any object that is being acted upon only by the force of gravity is said to be in a state of free fall. There are two important motion characteristics that are true of free-falling objects: • Free-falling objects do not encounter air resistance. • All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s (often approximated as 10 m/s/s for back-of-the-envelope calculations) Because free-falling objects are accelerating downwards at a rate of 9.8 m/s/s, a ticker tape trace or dot diagram of its motion would depict an acceleration. The dot diagram at the right depicts the acceleration of a free-falling object. The position of the object at regular time intervals - say, every 0.1 second - is shown. The fact that the distance that the object travels every interval of time is increasing is a sure sign that the ball is speeding up as it falls downward. Recall from an earlier lesson, that if an object travels downward and speeds up, then its acceleration is downward. Free-fall acceleration is often witnessed in a physics classroom by means of an ever-popular strobe light demonstration. The room is darkened and a jug full of water is connected by a tube to a medicine dropper. The dropper drips water and the strobe illuminate the falling droplets at a regular rate - say once every 0.2 seconds. Instead of seeing a stream of water free-falling from the medicine dropper, several consecutive drops with increasing separation distance are seen. The pattern of drops resembles the dot diagram shown in the graphic at the right. The Acceleration of Gravity It was learned in the previous part of this lesson that a free-falling object is an object that is falling under the sole influence of gravity. A free-falling object has an acceleration of 9.8 m/s/s, downward (on Earth). This numerical value for the acceleration of a free-falling object is such an important value that it is given a special name. It is known as the acceleration of gravity - the acceleration for any object moving under the sole influence of gravity. A matter of fact, this quantity known as the acceleration of gravity is such an important quantity that physicists have a special symbol to denote it - the symbol g. The numerical value for the acceleration of gravity is most accurately known as 9.8 m/s2. There are slight variations in this numerical value (to the second decimal place) that are dependent primarily upon on altitude. We will occasionally use the approximated value of 10 m/s2 in order to reduce the complexity of the many mathematical tasks that we will perform with this number. By so doing, we will be able to better focus on the conceptual nature of physics without too much of a sacrifice in numerical accuracy. g = 9.8 m/s2, downward Look It Up! Even on the surface of the Earth, there are local variations in the value of the acceleration of gravity (g). These variations are due to latitude, altitude and the local geological structure of the region. Recall from an earlier lesson that acceleration is the rate at which an object changes its velocity. It is the ratio of velocity change to time between any two points in an object's path. To accelerate at 9.8 m/s2 means to change the velocity by 9.8 m/s each second. If the velocity and time for a free-falling object being dropped from a position of rest were tabulated, then one would note the following pattern. Time (s) Velocity (m/s) 0 0 1 - 9.8 2 - 19.6 3 - 29.4 4 - 39.2 5 - 49.0 . Observe that the velocity-time data above reveal that the object's velocity is changing by 9.8 m/s each consecutive second. That is, the free-falling object has an acceleration of approximately 9.8 m/s2. Another way to represent this acceleration of 9.8 m/s2 is to add numbers to our dot diagram that we saw earlier in this lesson. The velocity of the ball is seen to increase as depicted in the diagram at the right. (NOTE: The diagram is not drawn to scale - in two seconds, the object would drop considerably further than the distance from shoulder to toes.) Representing Free Fall by Graphs • Early in Lesson 1 it was mentioned that there are a variety of means of describing the motion of objects. One such means of describing the motion of objects is through the use of graphs - position versus time and velocity vs. time graphs. In this part of Lesson 5, the motion of a free-falling motion will be represented using these two basic types of graphs. Representing Free Fall by Position-Time Graphs A position versus time graph for a free-falling object is shown below. Observe that the line on the graph curves. As learned earlier, a curved line on a position versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration (g = 9.8 m/s/s), it would be expected that its position-time graph would be curved. A further look at the position-time graph reveals that the object starts with a small velocity (slow) and finishes with a large velocity (fast). Since the slope of any position vs. time graph is the velocity of the object (as learned in Lesson 3), the small initial slope indicates a small initial velocity and the large final slope indicates a large final velocity. Finally, the negative slope of the line indicates a negative (i.e., downward) velocity. Representing Free Fall by Velocity-Time Graphs A velocity versus time graph for a free-falling object is shown below. Observe that the line on the graph is a straight, diagonal line. As learned earlier, a diagonal line on a velocity versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration (g = 9,8 m/s/s, downward), it would be expected that its velocity-time graph would be diagonal. A further look at the velocity-time graph reveals that the object starts with a zero velocity (as read from the graph) and finishes with a large, negative velocity; that is, the object is moving in the negative direction and speeding up. An object that is moving in the negative direction and speeding up is said to have a negative acceleration (if necessary, review the vector nature of acceleration). Since the slope of any velocity versus time graph is the acceleration of the object (as learned in Lesson 4), the constant, negative slope indicates a constant, negative acceleration. This analysis of the slope on the graph is consistent with the motion of a free-falling object - an object moving with a constant acceleration of 9.8 m/s/s in the downward direction. The Kinematic Equations The goal of this first unit has been to investigate the variety of means by which the motion of objects can be described. The variety of representations that we have investigated includes verbal representations, pictorial representations, numerical representations, and graphical representations (position-time graphs and velocity-time graphs). In Lesson 6, we will investigate the use of equations to describe and represent the motion of objects. These equations are known as kinematic equations. There are a variety of quantities associated with the motion of objects - displacement (and distance), velocity (and speed), acceleration, and time. Knowledge of each of these quantities provides descriptive information about an object's motion. For example, if a car is known to move with a constant velocity of 22.0 m/s, North for 12.0 seconds for a northward displacement of 264 meters, then the motion of the car is fully described. And if a second car is known to accelerate from a rest position with an eastward acceleration of 3.0 m/s2 for a time of 8.0 seconds, providing a final velocity of 24 m/s, East and an eastward displacement of 96 meters, then the motion of this car is fully described. These two statements provide a complete description of the motion of an object. However, such completeness is not always known. It is often the case that only a few parameters of an object's motion are known, while the rest are unknown. For example as you approach the stoplight, you might know that your car has a velocity of 22 m/s, East and is capable of a skidding acceleration of 8.0 m/s2, West. However you do not know the displacement that your car would experience if you were to slam on your brakes and skid to a stop; and you do not know the time required to skid to a stop. In such an instance as this, the unknown parameters can be determined using physics principles and mathematical equations (the kinematic equations). The BIG 4 The kinematic equations are a set of four equations that can be utilized to predict unknown information about an object's motion if other information is known. The equations can be utilized for any motion that can be described as being either a constant velocity motion (an acceleration of 0 m/s/s) or a constant acceleration motion. They can never be used over any time period during which the acceleration is changing. Each of the kinematic equations include four variables. If the values of three of the four variables are known, then the value of the fourth variable can be calculated. In this manner, the kinematic equations provide a useful means of predicting information about an object's motion if other information is known. For example, if the acceleration value and the initial and final velocity values of a skidding car is known, then the displacement of the car and the time can be predicted using the kinematic equations. Lesson 6 of this unit will focus upon the use of the kinematic equations to predict the numerical values of unknown quantities for an object's motion. The four kinematic equations that describe an object's motion are: There are a variety of symbols used in the above equations. Each symbol has its own specific meaning. The symbol d stands for the displacement of the object. The symbol t stands for the time for which the object moved. The symbol a stands for the acceleration of the object. And the symbol v stands for the velocity of the object; a subscript of i after the v (as in vi) indicates that the velocity value is the initial velocity value and a subscript of f (as in vf) indicates that the velocity value is the final velocity value. Each of these four equations appropriately describes the mathematical relationship between the parameters of an object's motion. As such, they can be used to predict unknown information about an object's motion if other information is known. In the next part of Lesson 6 we will investigate the process of doing this. Kinematic Equations and Problem-Solving The four kinematic equations that describe the mathematical relationship between the parameters that describe an object's motion were introduced in the previous part of Lesson 6. The four kinematic equations are: In the above equations, the symbol d stands for the displacement of the object. The symbol t stands for the time for which the object moved. The symbol a stand for the acceleration of the object. And the symbol v stands for the instantaneous velocity of the object; a subscript of i after the v (as in vi) indicates that the velocity value is the initial velocity value and a subscript of f (as in vf) indicates that the velocity value is the final velocity value. Problem-Solving Strategy In this part of Lesson 6 we will investigate the process of using the equations to determine unknown information about an object's motion. The process involves the use of a problem-solving strategy that will be used throughout the course. The strategy involves the following steps: 1. Construct an informative diagram of the physical situation. 2. Identify and list the given information in variable form. 3. Identify and list the unknown information in variable form. 4. Identify and list the equation that will be used to determine unknown information from known information. 5. Substitute known values into the equation and use appropriate algebraic steps to solve for the unknown information. 6. Check your answer to ensure that it is reasonable and mathematically correct. The use of this problem-solving strategy in the solution of the following problem is modeled in Examples A and B below. Example Problem A . Ima Hurryin is approaching a stoplight moving with a velocity of +30.0 m/s. The light turns yellow, and Ima applies the brakes and skids to a stop. If Ima's acceleration is -8.00 m/s2, then determine the displacement of the car during the skidding process. (Note that the direction of the velocity and the acceleration vectors are denoted by a + and a - sign.) The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. Note that the vf value can be inferred to be 0 m/s since Ima's car comes to a stop. The initial velocity (vi) of the car is +30.0 m/s since this is the velocity at the beginning of the motion (the skidding motion). And the acceleration (a) of the car is given as - 8.00 m/s2. (Always pay careful attention to the + and - signs for the given quantities.) The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown quantity. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = +30.0 m/s vf = 0 m/s a = - 8.00 m/s2 d = ?? The next step of the strategy involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. In general, you will always choose the equation that contains the three known and the one unknown variable. In this specific case, the three known variables and the one unknown variable are vf, vi, a, and d. Thus, you will look for an equation that has these four variables listed in it. An inspection of the four equations above reveals that the equation on the top right contains all four variables. vf2 = vi2 + 2 • a • d Once the equation is identified and written down, the next step of the strategy involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. (0 m/s)2 = (30.0 m/s)2 + 2 • (-8.00 m/s2) • d 0 m2/s2 = 900 m2/s2 + (-16.0 m/s2) • d (16.0 m/s2) • d = 900 m2/s2 - 0 m2/s2 (16.0 m/s2)*d = 900 m2/s2 d = (900 m2/s2)/ (16.0 m/s2) d = (900 m2/s2)/ (16.0 m/s2) d = 56.3 m The solution above reveals that the car will skid a distance of 56.3 meters. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. It takes a car a considerable distance to skid from 30.0 m/s (approximately 65 mi/hr) to a stop. The calculated distance is approximately one-half a football field, making this a very reasonable skidding distance. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed it is! Example Problem B Ben Rushin is waiting at a stoplight. When it finally turns green, Ben accelerated from rest at a rate of a 6.00 m/s2 for a time of 4.10 seconds. Determine the displacement of Ben's car during this time period. Once more, the solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step of the strategy involves the identification and listing of known information in variable form. Note that the vi value can be inferred to be 0 m/s since Ben's car is initially at rest. The acceleration (a) of the car is 6.00 m/s2. And the time (t) is given as 4.10 s. The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown information. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 0 m/s t = 4.10 s a = 6.00 m/s2 d = ?? The next step of the strategy involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. Again, you will always search for an equation that contains the three known variables and the one unknown variable. In this specific case, the three known variables and the one unknown variable are t, vi, a, and d. An inspection of the four equations above reveals that the equation on the top left contains all four variables. d = vi • t + ½ • a • t2 Once the equation is identified and written down, the next step of the strategy involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. d = (0 m/s) • (4.1 s) + ½ • (6.00 m/s2) • (4.10 s)2 d = (0 m) + ½ • (6.00 m/s2) • (16.81 s2) d = 0 m + 50.43 m d = 50.4 m The solution above reveals that the car will travel a distance of 50.4 meters. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. A car with an acceleration of 6.00 m/s/s will reach a speed of approximately 24 m/s (approximately 50 mi/hr) in 4.10 s. The distance over which such a car would be displaced during this time period would be approximately one-half a football field, making this a very reasonable distance. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed, it is! The two example problems above illustrate how the kinematic equations can be combined with a simple problem-solving strategy to predict unknown motion parameters for a moving object. Provided that three motion parameters are known, any of the remaining values can be determined. In the next part of Lesson 6, we will see how this strategy can be applied to free fall situations. Or if interested, you can try some practice problems and check your answer against the given solutions. Kinematic Equations and Free Fall As mentioned in Lesson 5, a free-falling object is an object that is falling under the sole influence of gravity. That is to say that any object that is moving and being acted upon only be the force of gravity is said to be "in a state of free fall." Such an object will experience a downward acceleration of 9.8 m/s/s. Whether the object is falling downward or rising upward towards its peak, if it is under the sole influence of gravity, then its acceleration value is 9.8 m/s/s. Like any moving object, the motion of an object in free fall can be described by four kinematic equations. The kinematic equations that describe any object's motion are: The symbols in the above equation have a specific meaning: the symbol d stands for the displacement; the symbol t stands for the time; the symbol a stands for the acceleration of the object; the symbol vi stands for the initial velocity value; and the symbol vf stands for the final velocity. Applying Free Fall Concepts to Problem-Solving There are a few conceptual characteristics of free fall motion that will be of value when using the equations to analyze free fall motion. These concepts are described as follows: • An object in free fall experiences an acceleration of -9.8 m/s/s. (The - sign indicates a downward acceleration.) Whether explicitly stated or not, the value of the acceleration in the kinematic equations is -9.8 m/s/s for any freely falling object. • If an object is merely dropped (as opposed to being thrown) from an elevated height, then the initial velocity of the object is 0 m/s. • If an object is projected upwards in a perfectly vertical direction, then it will slow down as it rises upward. The instant at which it reaches the peak of its trajectory, its velocity is 0 m/s. This value can be used as one of the motion parameters in the kinematic equations; for example, the final velocity (vf) after traveling to the peak would be assigned a value of 0 m/s. • If an object is projected upwards in a perfectly vertical direction, then the velocity at which it is projected is equal in magnitude and opposite in sign to the velocity that it has when it returns to the same height. That is, a ball projected vertically with an upward velocity of +30 m/s will have a downward velocity of -30 m/s when it returns to the same height. These four principles and the four kinematic equations can be combined to solve problems involving the motion of free-falling objects. The two examples below illustrate application of free fall principles to kinematic problem-solving. In each example, the problem solving strategy that was introduced earlier in this lesson will be utilized. Example Problem A Luke Autbeloe drops a pile of roof shingles from the top of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground. The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. You might note that in the statement of the problem, there is only one piece of numerical information explicitly stated: 8.52 meters. The displacement (d) of the shingles is -8.52 m. (The - sign indicates that the displacement is downward). The remaining information must be extracted from the problem statement based upon your understanding of the above principles. For example, the vi value can be inferred to be 0 m/s since the shingles are dropped (released from rest; see note above). And the acceleration (a) of the shingles can be inferred to be -9.8 m/s2 since the shingles are free-falling (see note above). (Always pay careful attention to the + and - signs for the given quantities.) The next step of the solution involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the time of fall. So t is the unknown quantity. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 0.0 m/s d = -8.52 m a = - 9.8 m/s2 t = ?? The next step involves identifying a kinematic equation that allows you to determine the unknown quantity. There are four kinematic equations to choose from. In general, you will always choose the equation that contains the three known and the one unknown variable. In this specific case, the three known variables and the one unknown variable are d, vi, a, and t. Thus, you will look for an equation that has these four variables listed in it. An inspection of the four equations above reveals that the equation on the top left contains all four variables. d = vi • t + ½ • a • t2 Once the equation is identified and written down, the next step involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. -8.52 m = (0 m/s) • (t) + ½ • (-9.8 m/s2) • (t)2 -8.52 m = (0 m) *(t) + (-4.9 m/s2) • (t)2 -8.52 m = (-4.9 m/s2) • (t)2 (-8.52 m)/(-4.9 m/s2) = t2 1.739 s2 = t2 t = 1.32 s The solution above reveals that the shingles will fall for a time of 1.32 seconds before hitting the ground. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. The shingles are falling a distance of approximately 10 yards (1 meter is pretty close to 1 yard); it seems that an answer between 1 and 2 seconds would be highly reasonable. The calculated time easily falls within this range of reasonability. Checking for accuracy involves substituting the calculated value back into the equation for time and insuring that the left side of the equation is equal to the right side of the equation. Indeed it is! Example Problem B Rex Things throws his mother's crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine the height to which the vase will rise above its initial height. Once more, the solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. You might note that in the statement of the problem, there is only one piece of numerical information explicitly stated: 26.2 m/s. The initial velocity (vi) of the vase is +26.2 m/s. (The + sign indicates that the initial velocity is an upwards velocity). The remaining information must be extracted from the problem statement based upon your understanding of the above principles. Note that the vf value can be inferred to be 0 m/s since the final state of the vase is the peak of its trajectory (see note above). The acceleration (a) of the vase is -9.8 m/s2 (see note above). The next step involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the vase (the height to which it rises above its starting height). So d is the unknown information. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 26.2 m/s vf = 0 m/s a = -9.8 m/s2 d = ?? The next step involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. Again, you will always search for an equation that contains the three known variables and the one unknown variable. In this specific case, the three known variables and the one unknown variable are vi, vf, a, and d. An inspection of the four equations above reveals that the equation on the top right contains all four variables. vf2 = vi2 + 2 • a • d Once the equation is identified and written down, the next step involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. (0 m/s)2 = (26.2 m/s)2 + 2 •(-9.8m/s2) •d 0 m2/s2 = 686.44 m2/s2 + (-19.6 m/s2) •d (-19.6 m/s2) • d = 0 m2/s2 -686.44 m2/s2 (-19.6 m/s2) • d = -686.44 m2/s2 d = (-686.44 m2/s2)/ (-19.6 m/s2) d = 35.0 m The solution above reveals that the vase will travel upwards for a displacement of 35.0 meters before reaching its peak. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. The vase is thrown with a speed of approximately 50 mi/hr (merely approximate 1 m/s to be equivalent to 2 mi/hr). Such a throw will never make it further than one football field in height (approximately 100 m), yet will surely make it past the 10-yard line (approximately 10 meters). The calculated answer certainly falls within this range of reasonability. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed, it is! Kinematic equations provide a useful means of determining the value of an unknown motion parameter if three motion parameters are known. In the case of a free-fall motion, the acceleration is often known. And in many cases, another motion parameter can be inferred through a solid knowledge of some basic kinematic principles.
Understanding Quantum Theory of Electrons in Atoms The goal of this section is to understand the electron orbitals (location of electrons in atoms), their different energies, and other properties. The use of quantum theory provides the best understanding to these topics. This knowledge is a precursor to chemical bonding. As was described previously, electrons in atoms can exist only on discrete energy levels but not between them. It is said that the energy of an electron in an atom is quantized, that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels. The energy levels are labeled with an n value, where n = 1, 2, 3, …. Generally speaking, the energy of an electron in an atom is greater for greater values of n. This number, n, is referred to as the principal quantum number. The principal quantum number defines the location of the energy level. It is essentially the same concept as the n in the Bohr atom description. Another name for the principal quantum number is the shell number. The shells of an atom can be thought of concentric circles radiating out from the nucleus. The electrons that belong to a specific shell are most likely to be found within the corresponding circular area. The further we proceed from the nucleus, the higher the shell number, and so the higher the energy level (Figure 9.4.1). The positively charged protons in the nucleus stabilize the electronic orbitals by electrostatic attraction between the positive charges of the protons and the negative charges of the electrons. So the further away the electron is from the nucleus, the greater the energy it has. This quantum mechanical model for where electrons reside in an atom can be used to look at electronic transitions, the events when an electron moves from one energy level to another. If the transition is to a higher energy level, energy is absorbed, and the energy change has a positive value. To obtain the amount of energy necessary for the transition to a higher energy level, a photon is absorbed by the atom. A transition to a lower energy level involves a release of energy, and the energy change is negative. This process is accompanied by emission of a photon by the atom. The following equation summarizes these relationships and is based on the hydrogen atom: The values nf and ni are the final and initial energy states of the electron. The principal quantum number is one of three quantum numbers used to characterize an orbital. An atomic orbital, which is distinct from an orbit, is a general region in an atom within which an electron is most probable to reside. The quantum mechanical model specifies the probability of finding an electron in the three-dimensional space around the nucleus and is based on solutions of the Schrödinger equation. In addition, the principal quantum number defines the energy of an electron in a hydrogen or hydrogen-like atom or an ion (an atom or an ion with only one electron) and the general region in which discrete energy levels of electrons in a multi-electron atoms and ions are located. Another quantum number is l, the angular momentum quantum number. It is an integer that defines the shape of the orbital, and takes on the values, l = 0, 1, 2, …, n – 1. This means that an orbital with n = 1 can have only one value of l, l = 0, whereas n = 2 permits l = 0 and l = 1, and so on. The principal quantum number defines the general size and energy of the orbital. The l value specifies the shape of the orbital. Orbitals with the same value of l form a subshell. In addition, the greater the angular momentum quantum number, the greater is the angular momentum of an electron at this orbital. Orbitals with l = 0 are called s orbitals (or the s subshells). The value l = 1 corresponds to the p orbitals. For a given n, p orbitals constitute a p subshell (e.g., 3p if n = 3). The orbitals with l = 2 are called the d orbitals, followed by the f-, g-, and h-orbitals for l = 3, 4, 5, and there are higher values we will not consider. There are certain distances from the nucleus at which the probability density of finding an electron located at a particular orbital is zero. In other words, the value of the wavefunction ψ is zero at this distance for this orbital. Such a value of radius r is called a radial node. The number of radial nodes in an orbital is n – l – 1. Consider the examples in Figure 9.4.2. The orbitals depicted are of the s type, thus l = 0 for all of them. It can be seen from the graphs of the probability densities that there are 1 – 0 – 1 = 0 places where the density is zero (nodes) for 1s (n = 1), 2 – 0 – 1 = 1 node for 2s, and 3 – 0 – 1 = 2 nodes for the 3s orbitals. The s subshell electron density distribution is spherical and the p subshell has a dumbbell shape. The d and f orbitals are more complex. These shapes represent the three-dimensional regions within which the electron is likely to be found. Principal quantum number (n) & Orbital angular momentum (l): The Orbital Subshell: https://youtu.be/ms7WR149fAY If an electron has an angular momentum (l ≠ 0), then this vector can point in different directions. In addition, the z component of the angular momentum can have more than one value. This means that if a magnetic field is applied in the z direction, orbitals with different values of the z component of the angular momentum will have different energies resulting from interacting with the field. The magnetic quantum number, called ml, specifies the z component of the angular momentum for a particular orbital. For example, for an s orbital, l = 0, and the only value of ml is zero. For p orbitals, l = 1, and ml can be equal to –1, 0, or +1. Generally speaking, ml can be equal to –l, –(l – 1), …, –1, 0, +1, …, (l – 1), l. The total number of possible orbitals with the same value of l (a subshell) is 2l + 1. Thus, there is one s-orbital for ml = 0, there are three p-orbitals for ml = 1, five d-orbitals for ml = 2, seven f-orbitals for ml = 3, and so forth. The principal quantum number defines the general value of the electronic energy. The angular momentum quantum number determines the shape of the orbital. And the magnetic quantum number specifies orientation of the orbital in space, as can be seen in Figure 9.4.3. Figure 9.4.4 illustrates the energy levels for various orbitals. The number before the orbital name (such as 2s, 3p, and so forth) stands for the principal quantum number, n. The letter in the orbital name defines the subshell with a specific angular momentum quantum number l = 0 for s orbitals, 1 for p orbitals, 2 for d orbitals. Finally, there are more than one possible orbitals for l ≥ 1, each corresponding to a specific value of ml. In the case of a hydrogen atom or a one-electron ion (such as He+, Li2+, and so on), energies of all the orbitals with the same n are the same. This is called a degeneracy, and the energy levels for the same principal quantum number, n, are called degenerate energy levels. However, in atoms with more than one electron, this degeneracy is eliminated by the electron–electron interactions, and orbitals that belong to different subshells have different energies. Orbitals within the same subshell (for example ns, np, nd, nf, such as 2p, 3s) are still degenerate and have the same energy. While the three quantum numbers discussed in the previous paragraphs work well for describing electron orbitals, some experiments showed that they were not sufficient to explain all observed results. It was demonstrated in the 1920s that when hydrogen-line spectra are examined at extremely high resolution, some lines are actually not single peaks but, rather, pairs of closely spaced lines. This is the so-called fine structure of the spectrum, and it implies that there are additional small differences in energies of electrons even when they are located in the same orbital. These observations led Samuel Goudsmit and George Uhlenbeck to propose that electrons have a fourth quantum number. They called this the spin quantum number, or ms. The other three quantum numbers, n, l, and ml, are properties of specific atomic orbitals that also define in what part of the space an electron is most likely to be located. Orbitals are a result of solving the Schrödinger equation for electrons in atoms. The electron spin is a different kind of property. It is a completely quantum phenomenon with no analogues in the classical realm. In addition, it cannot be derived from solving the Schrödinger equation and is not related to the normal spatial coordinates (such as the Cartesian x, y, and z). Electron spin describes an intrinsic electron “rotation” or “spinning.” Each electron acts as a tiny magnet or a tiny rotating object with an angular momentum, even though this rotation cannot be observed in terms of the spatial coordinates. The magnitude of the overall electron spin can only have one value, and an electron can only “spin” in one of two quantized states. One is termed the α state, with the z component of the spin being in the positive direction of the z axis. This corresponds to the spin quantum number ms=12. The other is called the β state, with the z component of the spin being negative and ms=−12. Any electron, regardless of the atomic orbital it is located in, can only have one of those two values of the spin quantum number. The energies of electrons having ms=−12 and ms=12 are different if an external magnetic field is applied. Figure 9.4.5 illustrates this phenomenon. An electron acts like a tiny magnet. Its moment is directed up (in the positive direction of the z axis) for the 12 spin quantum number and down (in the negative z direction) for the spin quantum number of −12. A magnet has a lower energy if its magnetic moment is aligned with the external magnetic field (the left electron) and a higher energy for the magnetic moment being opposite to the applied field. This is why an electron with ms=12 has a slightly lower energy in an external field in the positive z direction, and an electron with ms=−12 has a slightly higher energy in the same field. This is true even for an electron occupying the same orbital in an atom. A spectral line corresponding to a transition for electrons from the same orbital but with different spin quantum numbers has two possible values of energy; thus, the line in the spectrum will show a fine structure splitting. The Pauli Exclusion Principle An electron in an atom is completely described by four quantum numbers: n, l, ml, and ms. The first three quantum numbers define the orbital and the fourth quantum number describes the intrinsic electron property called spin. An Austrian physicist Wolfgang Pauli formulated a general principle that gives the last piece of information that we need to understand the general behavior of electrons in atoms. The Pauli exclusion principle can be formulated as follows: No two electrons in the same atom can have exactly the same set of all the four quantum numbers. What this means is that electrons can share the same orbital (the same set of the quantum numbers n, l, and ml), but only if their spin quantum numbers ms have different values. Since the spin quantum number can only have two values (±12), no more than two electrons can occupy the same orbital (and if two electrons are located in the same orbital, they must have opposite spins). Therefore, any atomic orbital can be populated by only zero, one, or two electrons. The properties and meaning of the quantum numbers of electrons in atoms are briefly
GRADE 4 Module 6 Lesson 3. Interpret Remainders This PowerPoint file contains instructional aids for teachers who have purchased Into Math. It is intended to be projected to students and used in conjunction with the Student Edition and manipulatives as needed. These slides can be used to move the conversation forward in the classroom, but they should not serve as a replacement for student-centered, collaborative conversations in which students have the space they need to find an entry point, construct meaning, and build understanding. About the Slide Presentation Presenter View: Use the Presenter view to see notes while presenting. Customization: Add or delete content or notes to get the best learning experience for your classroom. 1 Problem of the Day. Which equations can be used to solve the following problem? Rita makes 40 bracelets and gives an equal number to 8 friends, including Veronica. Veronica gives 2 of the bracelets that she received to her sister. How many bracelets does Veronica have left? A. 40 – 8 = 32 32 ÷ 2 = 16 B. 40 ÷ 8 = 5 5 + 2 = 7 C. 8 + 2 = 10 40 ÷ 10 = 4 D. 40 ÷ 8 = 5 5 – 2 = 3 2 I Can. I Can solve a division problem and interpret the remainder in the context of the problem. 3 Spark Your Learning. Aiden is building solar toy cars in his science club. The cars collect and use energy from the sun for power. Aiden buys 18 wheels. Each car needs 4 wheels. How many cars can Aiden build? Show your thinking. 4 Turn and Talk. What is the remainder in this problem? What does the remainder mean? Professional Development note: Use the Professional Learning Cards to provide language routines that may help students access the meaning of the problem. 5 Build Understanding • Task 1 ACTIVITY. There are 57 students going to the science museum. Each van can take 5 students. How many vans are needed to take all the students? Use a visual model to show how the students are divided into groups of 5. 6 Turn and Talk. How can you use the whole-number quotient and remainder to answer these questions? How many vans will be full? How many students will ride in the van that is not full? Professional Development note: Use the Professional Learning Cards to provide language routines that may help students access the meaning of the problem. 7 Step It Out • Task 2 ACTIVITY.. Amanda has 73 inches of wire for a science experiment. She needs to cut all the wire into 8 identical pieces. How many inches long will each piece be? 8 Turn and Talk. Why is this problem a good situation to write the remainder as a fraction? Professional Development note: Use the Professional Learning Cards to provide language routines that may help students access the meaning of the problem. 9 Check Understanding. 1. Maya needs 44 batteries for smoke alarms. The batteries come in packs of 6. How many packs does Maya need to buy? For 44 ÷ 6, the whole-number quotient is ____ and the remainder is ____. Maya needs to buy ____ packs. Circle how you interpreted the remainder to solve the problem. 10 I Can Scale. 4 I can explain how to solve a division problem and interpret the remainder in the context of the problem. 3 I can solve a division problem and interpret the remainder in the context of the problem. 2 I can solve a division problem and identify the whole-number quotient and the remainder. 1 I can solve a division problem with a remainder. 11 Exit Ticket. Mr. Jenkins’ class is giving speeches during a 46-minute class. Each student will be able to talk for 4 minutes. How many students can give speeches? Justify your answer.
A solution is a mixture in which one or more substances are uniformly distributed in another substance. Solutions can be mixtures of liquids, solids, or gases. For example, plasma, the liquid part of blood, is a very complex solution. It is composed of many types of ions and large molecules, as well as gases, that are dissolved in water. A solute (SAHL-YOOT) is a substance dissolved in the solvent. The particles that compose a solute may be ions, atoms, or molecules. The solvent is the substance in which the solute is dissolved. For example, when sugar, a solute, and water, a solvent, are mixed, a solution of sugar water results. Though the sugar dissolves in the water, neither the sugar molecules nor the water molecules are altered chemically. If the water is boiled away, the sugar molecules remain and are unchanged. Solutions can be composed of various proportions of a given solute in a given solvent. Thus, solutions can vary in concentra- tion. The concentration of a solution is the amount of solute dis- solved in a fixed amount of the solution. For example, a 2 percent saltwater solution contains 2 g of salt dissolved in enough water to make 100 mL of solution. The more solute dissolved, the greater is the concentration of the solution. A saturated solution is one in which no more solute can dissolve. Aqueous (AY-kwee-uhs) solutions—solutions in which water is the solvent—are universally important to living things. Marine microorganisms spend their lives immersed in the sea, an aqueous solution. Most nutrients that plants need are in aqueous solutions in moist soil. Body cells exist in an aqueous solution of intercellu- lar fluid and are themselves filled with fluid; in fact, most chemical reactions that occur in the body occur in aqueous solutions. Copyright © by Holt, Rinehart and Winston. All rights reserved. Liquid water Solid water Ice (solid water) is less dense than liquid water because of the structure of ice crystals. The water molecules in ice are bonded to each other in a way that creates large amounts of open space between the molecules, relative to liquid water. FIGURE 2-12 solvent from the Latin solvere, meaning “to loosen” Word Roots and Origins CHEMISTRY OF LIFE 43 ACIDS AND BASES One of the most important aspects of a living system is the degree of its acidity or alkalinity. What do we mean when we use the terms acid and base? Ionization of Water As water molecules move about, they bump into one another. Some of these collisions are strong enough to result in a chemical change: one water molecule loses a proton (a hydrogen nucleus), and the other gains this proton. This reaction really occurs in two steps. First, one molecule of water pulls apart another water molecule, or dissociates, into two ions of opposite charge: H2O ∏ H OH The OH ion is known as the hydroxide ion. The free H ion can react with another water molecule, as shown in the equation below. H H2O ∏ H3O The H3O ion is known as the hydronium ion. Acidity or alkalin- ity is a measure of the relative amounts of hydronium ions and hydroxide ions dissolved in a solution. If the number of hydronium ions in a solution equals the number of hydroxide ions, the solution is said to be neutral. Pure water contains equal numbers of hydro- nium ions and hydroxide ions and is therefore a neutral solution. Acids If the number of hydronium ions in a solution is greater than the number of hydroxide ions, the solution is an acid. For example, when hydrogen chloride gas, HCl, is dissolved in water, its mol- ecules dissociate to form hydrogen ions, H, and chloride ions, Cl, as is shown in the equation below. HCl ∏ H Cl These free hydrogen ions combine with water molecules to form hydronium ions, H3O. This aqueous solution contains many more hydronium ions than it does hydroxide ions, making it an acidic solution. Acids tend to have a sour taste; how- ever, never taste a substance to test it for acidity. In concentrated forms, they are highly corrosive to some materials, as you can see in Figure 2-13. Bases If sodium hydroxide, NaOH, a solid, is dissolved in water, it dissociates to form sodium ions, Na, and hydroxide ions, OH, as shown in the equation below. NaOH ∏ Na OH Copyright © by Holt, Rinehart and Winston. All rights reserved. Eco Connection onnection Acid Precipitation Acid precipitation, more commonly called acid rain, describes rain, snow, sleet, or fog that contains high levels of sulfuric and nitric acids. These acids form when sulfur dioxide gas, SO2, and nitrogen oxide gas, NO, react with water in the atmosphere to produce sulfuric acid, H2SO4, and nitric acid, HNO3. Acid precipitation makes soil and bodies of water, such as lakes, more acidic than normal. These high acid levels can harm plant and animal life directly. A high level of acid in a lake may kill mollusks, fish, and amphibians. Even in a lake that does not have a very elevated level of acid, acid precipitation may leach aluminum and magnesium from soils, poisoning water- dwelling species. Reducing fossil-fuel consump- tion, such as occurs in gasoline engines and coal-burning power plants, should reduce high acid levels in precipitation. Sulfur dioxide, SO2, which is produced when fossil fuels are burned, reacts with water in the atmosphere to produce acid precipitation. Acid precipitation, or acid rain, can make lakes and rivers too acidic to support life and can even corrode stone, such as the face of this statue. FIGURE 2-13 44 CHAPTER 2 This solution then contains more hydroxide ions than hydronium ions and is therefore defined as a base. The adjective alkaline refers to bases. Bases have a bitter taste; however, never taste a substance to test for alkalinity. They tend to feel slippery because the OH ions react with the oil on our skin to form a soap. In fact, commercial soap is the product of a reaction between a base and a fat. pH Scientists have developed a scale for comparing the relative con- centrations of hydronium ions and hydroxide ions in a solution. This scale is called the pH scale, and it ranges from 0 to 14, as shown in Figure 2-14. A solution with a pH of 0 is very acidic, a solution with a pH of 7 is neutral, and a solution with a pH of 14 is very basic. A solution’s pH is measured on a logarithmic scale. That is, the change of one pH unit reflects a 10-fold change in the acidity or alkalinity. For example, urine has 10 times the H3O ions at a pH of 6 than water does at a pH of 7. Vinegar, has 1,000 times more H3O ions at a pH of 3 than urine at a pH of 6, and 10,000 times more H3O ions than water at a pH of 7. The pH of a solution can be measured with litmus paper or with some other chemical indicator that changes color at various pH levels. Buffers The control of pH is important for living systems. Enzymes can function only within a very narrow pH range. The control of pH in organisms is often accomplished with buffers. Buffers are chemi- cal substances that neutralize small amounts of either an acid or a base added to a solution. As Figure 2-14 shows, the composition of your internal environment—in terms of acidity and alkalinity— varies greatly. Some of your body fluids, such as stomach acid and urine, are acidic. Others, such as intestinal fluid and blood, are
MEANING OF POLLUTION Pollution is the release of harmful substances into the environment and making it unsafe for human and animals. TYPES OF POLLUTION 1. WATER POLLUTION: This is the release of harmful substances into bodies of water. Examples of water pollutants are urine, bathing, excretion from man and animals, dumping of refuse into the rivers, lakes etc. 2. AIR POLLUTION: This is the release of harmful substances into the atmosphere making it unfit to breathe in. Examples of air pollutants are : smoke of vehicles, smoke from industries, oil burning, smoke from firewood, dead animals etc. 3. NOISE POLLUTION: This is a kind of pollution from the constant loudness of music or rowdiness. It disturbs the mind and prevents people from sleeping, resting or reasoning properly. THE FOLLOWING ARE THE EFFECTS OF POLLUTION 1. It makes the water unfit for drinking 2. It causes dysentery, typhoid fever and cholera. 3. It causes sneezing, blood poisoning, cough and lung diseases. 4. It causes headaches and sleeplessness. 5. It makes the air dirty and bad for breathing into the body. CONTROL OF POLLUTION ARE AS FOLLOWS: 1. Refuse should be dump in a proper place 2. Industries should be located far away from where people live. 3. Modern toilets should be built. 4. Regular cleaning of the surroundings.
Directions :Identify the meaning of the unfamiliar words through context clues.