What analogy is used to explain the interaction between lower and higher dimensions?

being on different floors of a building

Why are higher dimensions difficult to visualize for humans?

we are third-dimensional beings

Higher Dimensions | Quizalize

Abstract The main focus of this research is to discuss the perspective of the teamwork and its impaction organizational performance and success. Also highlight the Meanings of Team and its work sprit towards batter organizational performance and specific to its impact on the success of organization that provided the basis for this research study. In this research study a thoroughly focus was on organization and teamwork. The aim of this research is to deliver a participative view of teamwork in the organization, and also discourses the major issues and emphases on the recent work that opens the basis to move research onward. There is much worth in taking a more focus on the essential areas of teamwork. The team signifies the spirit and working capacity of the employees as team to bring organization to the success. The various explanations, definitions, processes, dimensions, team size and benefits etc. regarding the above topic teamwork and organizational success is highlighted. Keywords: Teamwork, Success, Organization, Performance, Work Groups, Employees Introduction It is indeed human beings have learned in their beginning of life to work together as (Team) that have made such a remarkable developments as unique specie. Human beings have experience throughout their social history, lived, loved, grow younger to older and worked together in groups said West M.A. (2012).The mutual social knowledge of living and functioning together creates connection among people, society and families. When work is done cooperatively as a team it can achieve extremely extra work than individually. Team can be defined as in the human society to live, to work and to play and to cooperate with others for particular task. According to John W. Newstrom et al (1993) “team is the process of assessing performance of workers, passing information and exploring methods to increase performance”. If observe closely, one can discover the instances of The Government: Research Journal of Political Science Supplementary Edition Vol. III 88 The Government social (teams) they are functioning either effectively or ineffectively everywhere; organizations, schools, work place, home etc. “Coordinating the events of people is like sand house, making by using a sole particles of sand” expressed Belbin, R. M.(2010). Moreover it is one of the general myths that the skill of team member is more important than their vigor, attention and determination for the tasks. Another widespread myth is that the team members are not alone accountable for the achievements or failures of their tasks the truth is that the members are the small parts in the teams and their individual abilities effect on the various results in team. The working relationships exist among team that might sight these relationships at different levels of involvement or relationships among the members as they move towards the degree of communication, integration and commitment increases. Terry L.G. et al (1980) expressed that “The skills are essential if members have to work together efficiently in complex situations, only development of skills and relationships, involvement on the task regarding the particular task might be selected for reaching at target that is considered as a definition of a team”. Team often perform higher when they work together with sprit that enable them to achieve a collective goal at the workplace, it is not only benefits to the organization also affects the workers confidence and success. Cooperating on various tasks reduces workloads for all team members and enables them to share duties or ideas. Work as a team is the part of everyone's life, as one is a member of a family team, staff team, school team, and community teams etc., so as to understand how to work effectively as a team member. Especially there is a need when task is threatened with increasingly many problems for example; the energy problem has effects on organization, family life, and social development and the multi-dimensional nature of many problems require a scientific skill based problem solving approach. Terry L.G, et al (1980) expressed that “The skills, competencies and efforts of team by setting priorities the team can have better impact on the problems solving such efforts can reduce work load, work duplication, and produce a result better than separate efforts”. There are some processes of teamwork by adopting those the objectives can be achieved easily. Le Pine, et al, (2008) identified10 teamwork processes that fall in three categories following are those. TEAMWORK PROCESSES TRANSITION PROCESSES •Mission analysis •Goal specification •Strategy formulation ACTION PROCESSES •Monitoring progress toward goals •Systems monitoring •Team monitoring and backup behavior •Coordination INTERPERSONAL PROCESSES •Conflict management •Motivation and confidence building •Affect management Team Work 89 Teamwork process reduces the work stress on every member which permits members to complete given important task of organization; teamwork offers members an opening to pledge with each other. Also it develops relations between the members who start a teamwork they usually sense appreciated on productive accomplishment of task. It may be cited one of the best instances of surgical team; where surgeon is assisted by his team; nurses, anesthetist and experts etc., everyone knows that their success depends upon the teamwork. In addition they are devoted to the aim that is human life it is easy to succeed with best teamwork. The important role of manager is the team building, trust building, confidence building, in the team to achieve the task. In the Situation where all team members contribute the task, it develops the positive relationship in the team that improves the trust of team members.“Functions effectively members of team must be flexible, committed, trusting each other and help to each other’s in the progress and the achievement of goals” Expressed Plamínek (2008). The accountability of every member in the team must be increased so that they do not let each other down therefore they do their best for the achievements of their teams. In contrast, working alone on a task the pressure is generally high in team in those cases of small confidence impacts fewer on members. Team consists on members who always vary from each other’s in skills, knowledge and abilities but working together that is an opportunity for them to gain skills and knowledge from each other’s that they had never before. Working alone on a task is a challenge and using the ideas of each other brings them to come up with a mutual resolution and the achievement of the task. Nowadays theoretical development and research has rested largely a new trend that is emerging within the organizations as an essential process of teamwork. Teamwork has brought a new move in the research and development to the inputs and outputs that bound, constrain and impact on the team processes within organizations said Ilgen, D.R. (1999). The world is changes fast, any one set of instructions can’t be sufficient, changes needs flexible members, teams and organizations so as to be effective on task. This paper suggests that in teams members must use the exclusive human abilities. Cannon B.et al (1995) has précised dimensions of teams into three categories: Team dimensions 1-Cognitions: include associations, task team-mate characteristics, team mission, objectives, norms, and resources, team role interaction patterns, skills, roles, and team orientation. 2-Skills: consist on adaptability, shared situational awareness and mutual concept to conflict resolution. 90 The Government 3-Attitudes: symbolize motivation, collective potency, shared vision, team cohesion, mutual trust, collective orientation and importance of. Teamsize Researchers have given different approvals about the best size of team as Katzenbachetet al (1993) suggested that the teams should comprise on a dozen or so members which are enough to achieve a task. Although seven is the best size of the team in the organizational practices said Scharf, A. (1989). Several views of researchers are expressed in the literatures and it is difficult to decide which better is because their opinions are based on their own observations. The team size matters in the proper output and performance however from an empirical research it is also difficult to decide the suitable team size and what to accept. This study suggests that team size has a practical link with efficacy such as few or many member shave impact on the performance but size matters. Proper size of team improves the performance maximum stated Campion M. A et al (1996).These different results are expected due to the fact that appropriate team size is required for task, environment and situation where team works. However, larger teams can also experience coordination problems that delay performance. Sheppard, J. A. (1993) expressed that the question of best team’s size is a complex one; more research is required on this topic to explain the impact of team size on given definite task. Literature Review Across many different organizations and industries teamwork is focused to increase the performance of employees’ their unity and also create work culture. Organizations those regularly develop new ideas or products using a project-based approach and assemble teams in order to focus responsibilities to achieve the object. Researchers have given dissimilar meanings of “teams”. Dyer W.G. (2007) said that “teams are groups of people who trust in cooperation, if members are expert the success of goal is more possible”. It is essential due to the problemsolving cooperation added from many minds of team members working on a resolution of problems. Team members contribute their thoughts together to make exclusive plans for dealing with problems and this unity enhance the result due to interaction, trust and teamwork. Teamwork means a "work done by several companions with each doing a part but all subordinating personal prominence to the efficiency of the whole" Merriam, (2012). In addition combined employees are expected less hostile to each other and accepting more of each other’s decisions. Unity of employees can increase the flow of work in organization. When employee’s working together as a team, they learn from each other that awareness is based on their personal experiences and from coworkers; Team Work 91 employees from different departments may acquire knowledge from each other. The main object for organizations is to hold the team effort to achieve output and quality; team is a key to achieve quality productivity. According to Maddux et al (2003) “some of the organizations have major benefits from the use of teamwork which are showed in the following chart: Benefits of Teamwork 1 Improving quality of work life for employees 2 Reducing absenteeism and increasing turnover 3 Increasing innovation and change 4 Improving organizational adaptability and flexibility A real team is mostly one where members are allowed to take decisions that how to complete task. That authority enables them to control the work process, decreases the outside control and increases the sense of duty for work. Team always feels superiority on workplace and they rely on each other’s being there. Plamínek (2008) said that “affiliation with teamwork gives member a sense of belonging, interaction and recognition of success”. These actions support to remove the sense of loneliness of team member in organization. Effective teams can also improve efficacy through communication and trust between the team members, quality of work and decrease in absenteeism contribute to positive impact on team. Involving employees in teamwork helps the organization remain open to new ideas.“The world of organizations is shifting individualism is out and collectivism is in, power is out, empowerment is in.” stated G. M. Parker (1998). This study discovers the experiences and difficulties of teamwork that employees and organizations are facing nowadays due to big transformation and enlarged globalization. In recent years a remarkable amendment has been emerged in the belief of team working organizations. The modern study has explored that the scope of teamwork have been appeared in system rooted in belief, and employees accept changes that denoting a modern organizational system. The organizations which are responsive to the changes appear to achieve greater satisfaction. Although it may be suggested that, the managers should assess the values and beliefs of their employees to play more dedicated role in the development of organization by making sprit to face the modern challenges. Organizational cultural is much significant and it has the excessive impact on the performance of organization and employees’ but it is quiet arguable topic that the culture of teamwork can be developed according to the requirement. It is difficult to specify the relationships and to assess the reliable set of values to use as they believed symbol across the entire organizations. This review study focus that 92 The Government there is a great influence of organizational culture on the assumptions, values, and beliefs on the individuals’ considerations, actions and performances and so is vice versa, through learning, and training process. However the researchers believe that the organizational setup aids to unite employees of diverse cultures and dissimilar social backgrounds, traditions and have their own beliefs to work. Creating a positive teamwork culture it has several diverse aspects are goal setting, conflict resolution, empowerment, ability to accomplish tasks, measuring output and consideration for other teamwork cultures stated Pack L, et al April 27, (2012). Team work in the organization delivers employees the wisdom of unity; understand to each other’s, and reducing conflict. In addition teamwork in organization inspires employee for impartiality by affirming that no one is ignored in the organization and all treated equally. It is known that a team in organization is bound and sincere to work with dedication to bring the success. If the employees are committed and recognize the teamwork values and its benefits, as a part of the organization they can contribute a lot to the achievement of organization. One can finds the informal instances of team at these level, family, society, community, tribe and work groups etc., and formally team appears at the level of departments, functional groups, and other organizational units. The employees feel a greater sense of achievement for being a part of an organization, if they attain team work, having freedom to work not forced. The system gives best performance to achieve recognition and credit from their managers and it will increase their effort that helps them to contribute the organizational performance. Each team batter knows about their role and how to achieve tasks. The true spirit of teamwork gives benefit to organization in maintaining its standard by which it becomes identified. The team defines its specialty, and the way it is doing task that is perceived by the organization as well as its managers and it is secured by appreciation. Employees identify what they believe; that exist in their belief system and those understandings call them to change their views to develop and raise attention towards batter performance. The literature contains sufficient definitions of teamwork and the word team is used to denote a set of generally developed as to learn collective values, attitudes and cooperation to work. The study praises that the teamwork is mostly related with the team success for instance, Wagner (1995) described that “in the team individual is less valued and group is more valued, with”. It is found in the study that individualismcollectivism both regulates the relationships between team size, standing, and cooperation that have better effects on the cooperation of individualists rather than the cooperation of collectivists. Team Work 93 Conclusion The main concentration of this research paper is to examine more in-depth the fundamental of teamwork and its effectiveness to achieve the organizational goals. Teamwork provides vast amounts of knowledge and information, cultural differences each of these building a culture of teamwork and the skill to make the valuable solutions of the problems. To work efficiently, team members need a good understanding of how to do their job, to achieve goal and for that a basic way to ensure understanding is training, then they have to be motivated to do a job. Team is a vital activity of organization, when organization desires to perform sound it has to be confident that team functions effectively. Consequently it is compulsory to know how team performs, what manners within a team happen, and how they make decisions. If there is knowhow of teamwork events, it can be effective for the tasks that they have to accomplish. Organizations build up their own culture through tradition, history and structure these values can be accepted by team workers of an organization. The values and assumptions are the vital tools of organizations and are used as guidance for team. These have to do mostly with the basic dignity and worth of all members of team and the ability, necessity for them to solve the problems and work for the positive change. Through this review study is concluded that there is a good impact of teamwork on the organizations doings and success. Subsequently in recently developed literature there is a great focus amongst the social scientists and scholars’ in their discussion on the above topic teamwork. The above study is also an evidence of little effort to assess the significance of teamwork in organizations success. teams in organiz

Health 11/12 Review for Final Exam Core Concepts - Mental and Emotional Health, Substance Abuse Prevention, Safety and Violence Prevention, Family Life and Human Sexuality, Disease Prevention and Control, Healthy Eating Health Education Skills - goal setting, decision making, accessing information/resources, analyzing influences, communication, self-management, advocacy DIMENSIONS of Wellness - social, spiritual, emotional/mental, environmental, financial, intellectual, multicultural, occupational, physical, sexual RISK factors - anything that increases the risk of disease, injury, or illness. PROTECTIVE factors - anything that decreases the risk of disease, injury, or illness. INTERNAL health factors - health factors that can be either hereditary and genetic or acquired elements -- include smoking and personal diet or eating habits. Example – a genetic predisposition to an illness. EXTERNAL health factors - health factors that are part of the direct outer environment, the geographical location, micro-organisms, socio-economic elements that could affect an individual's health. Example – being unable to afford mental health services. Unit 1- Managing Personal and Community Wellness Explain Maslow’s Hierarchy of Needs in your own words using the image provided. Explain how each Social Determinant of Health may impact a person’s health. Levels of Disease Prevention • PRIMARY The goal is to avoid conditions altogether. • SECONDARY The goal is early detection. • TERTIARY The goal is to minimize the damage (manage). Define the following terms. Fads/Trends Sleep hygiene Driver safety Unit 2- Investigating Social Ecological Factors on Well-Being Socio-Ecological Model – The SEM examines how health behaviors form based on characteristics of individuals, communities, nations and levels in between. Each level overlaps with other levels signifying how the best public health strategies are those that encompass and target a wide range of perspectives. Interpersonal (personal) health vs. intrapersonal (relationship) health Health INEQUITY - systemic, ingrained and unjust barriers that prevent segments of the population from having the opportunity of health leading to health disparity. IMPLICIT BIAS - a form of bias that occurs automatically and unintentionally, that nevertheless affects judgments, decisions, and behaviors. Research has shown implicit bias can contribute to unequal access to quality healthcare, negative patient-provider relationships and interactions; and create mistrust in the healthcare system and practitioners among patients. This can contribute to health disparities. Health DISPARITY - represents a difference in health between populations. It is often used to describe disease burden and other negative health outcomes socially disadvantaged groups may face. Health EQUITY - The opposite of health inequity. It describes a system that supports a high standard of health and healthcare for all people. Racism - Beliefs, attitudes, institutional arrangements, and acts that tend to denigrate individuals or groups because of phenotypic characteristics or ethnic group affiliation. DISCRIMINATION - An unjust differential treatment of a person or a group. PRIVILEGE- The unearned access to resources and social power that are only available to some because of their membership within certain social groups. OPPRESSION is the act of taking away choices from others and can be defined as a system that maintains advantage and disadvantage based on social identities and that acts on multiple levels from interpersonal to institutional and societal. (internalized, interpersonal, institutional, structural) Systematic Oppression - Intentional disadvantage of groups of people based on their identity while advantaging members of dominant group (race, gender, sexual orientation, language, size, ability, etc.). Intersectionality - The complex, cumulative way in which the effects of multiple forms of discrimination (such as racism, sexism, and classism) combine, overlap, or intersect especially in the experiences of marginalized individuals or groups Unit 3- Accessing Resources and Communicating to Support Mental and Emotional Health What is anger? What is anxiety? What is stress? STRESSORS are the things that cause stress. Stressors can be internal and external. A stressor may be a one-time or short-term occurrence, or it can happen repeatedly over a long time. INTERNAL Stressors - are made by your belief system and the way you evaluate yourself. Examples include pessimistic attitude, negative self-talk, deep need to be perfect, low self-esteem or body image, unhealthy standards for self. EXTERNAL Stressors - are stressful things that happen in your surroundings and/or in your environment. Examples include busy schedules, work problems, family issues, financial trouble, social problems, injury, unforeseen circumstances. Socio-economic issues are also a part of external stressors such as poverty, violence, and racism. Define the following mental health conditions. Depression Eating disorders NSSI Non-suicidal self-injury Grief/Loss Suicide prevention A.C.T. • ACKNOWLEDGE- Tell them in a caring way that you recognize that they are having a problem • CARE- You can show you care by actively listening - put away anything else you are doing, make eye contact, sit down, ask questions. • TELL-(call 988 for additional help and support) - Tell them it is important that they speak with a trusted adult. Help them figure out who this may be and offer to go with your friend. A social norm is an unwritten, informal rule meant to guide behavior among the of society. It distinguishes between acceptable and unacceptable, good and bad, and so on. Social norms can influence a person with emotional or mental health disorders, access to care and stigmatize their situation. STIGMA- a mark of disgrace associated with a particular circumstance, quality, or person. • Self-stigma - This describes the internalized stigma that people with mental health conditions feel about themselves. • Public stigma - This refers to the negative attitudes around mental health from people in society. • Institutional stigma - This is a type of systemic stigma that arises from corporations, governments, and other institutions. Unit 4- Evaluating Risks of Substance Use and Abuse Harm Reduction - a set of practical strategies and ideas aimed at reducing negative consequences associated with drug use. Explain how each level of the Social Ecological Model is impacted by addiction. Individual Relationship Community Society SEM Level Contributing/Risk Factors to substance use Preventative/Protective Factors for substance use Individual Interpersonal/Relationship Community Society Unit 5- Analyzing Influences to Examine Ways to Increase Safety and Reduce Violence HATE CRIME - a crime, usually violent, motivated by prejudice or intolerance toward an individual’s national origin, ethnicity, color, religion, gender, gender identity, sexual orientation, or disability. Explain how the media influences violence in society. The Pyramid of Hate Explain the escalation of hate using the Pyramid of Hate visual. List several hate crime motivators. Example: age HEALTHY Relationship Signs - comfortable pace, trust, honesty, independence, respect, equality, kindness, taking responsibility, healthy conflict, fun UNHEALTHY Relationship Signs - intensity, possessiveness, manipulation, isolation, sabotage, belittling, guilting, volatility, deflecting responsibility, betrayal Sexual Assault is a sexual behavior WITHOUT consent. Human trafficking - the recruitment, harboring, transportation, provision, or obtaining of a person for labor or services, using force, fraud, or coercion for the purpose of subjection to involuntary servitude, peonage, debt bondage, or slavery. Sex trafficking - commercial sex act induced by force, fraud, or coercion, or in which the person induced to perform such an act has not attained 18 years of age. Trafficking happens using… • Force - using violence to control someone. • Fraud - using lies to control someone. • Coercion - using threats to control someone. Unit 6- Family Life and Human Sexuality Agency - A belief about yourself and the extent to which you can act on that belief. • The ability to choose freely one’s own narrative. • To embrace the idea that I am the cause (or agent) of my own thoughts and actions. • Personal agency is a personal responsibility for who we are, what we experience, what we do about that experience, and how we shape our world to give us more of the experiences we want. SEXUAL Agency • The ability to choose your own interests and desires vs. what we see in the media or others’ perceptions • The ability to identify, communicate, and negotiate one’s sexual needs • The ability to initiate behaviors that allow for the satisfaction of those needs Sexually Explicit Material - photographs, videos, films, magazines, and books whose primary themes, topics, or depictions involve sexuality that may cause sexual arousal. Sexual scripts - thoughts, patterns, or behavior that a person has about themselves in a romantic or sexual context. It is how people picture themselves or want to project themselves in front of others. Reproductive Rights of Teens - In Maryland, teens have the right to an abortion, keep their child, obtain and use birth control, paternity tests, adoption, give up custody of their child within 10 days of birth (Safe Haven Law). • REPRODUCTIVE RIGHTS- legal rights and the freedom of the individual to control decisions regarding contraception, abortion, sterilization and childbirth. • SAFE HAVEN LAW- a distressed parent who is unable or unwilling to care for their infant can safely give up custody of their baby, no questions asked. CONSENT is an agreement between participants to engage in sexual activity. • It is clearly and freely communicated, verbal, and affirmative. Consent CANNOT be given if… • A person is underage, one or both partners is intoxicated or incapacitated by drugs or alcohol, one partner is asleep or unconscious, one partner feels pressured, threatened or intimidated, or one partner holds a position of power or authority over the other. Unit 7- Advocating for Enhanced Nutrition, Food Systems, and Health Outcomes Dietary Guidelines for Americans Guideline 1: Follow a Healthy Dietary Pattern at Every Life Stage Guideline 2: Customize and Enjoy Food and Beverage Choices to Reflect Personal Preferences, Cultural Traditions, and Budgetary Considerations Guideline 3: Focus on Meeting Food Group Needs with Nutrient-Dense Foods and Beverages, and Stay Within Calorie Limits Guideline 4: Limit Foods and Beverages Higher in Added Sugars, Saturated Fat, and Sodium, and Limit Alcoholic Beverages FOOD DESERT- a neighborhood where there is little or limited access to healthy and affordable food such as fruits, vegetables, whole grains, low-fat milk and other foods that make up the full range of a healthy diet. FOOD INSEQURITY lack of access to a sufficient amount of food because of limited funds. More than 49 million American households are considered food insecure and are vulnerable to poor health as a result. PROCCESED FOODS- any raw agricultural commodities that have been washed, cleaned, milled, cut, chopped, heated, pasteurized, blanched, cooked, canned, frozen, dried, dehydrated, mixed or packaged — anything done to them that alters their natural state.

Forces in two dimensions (including resolution of a force)

Forces in two dimensions

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

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