Number of Solutions of an Equation

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

Electrostatics The section of CBSE Class 12 Physics electrostatic potential and capacitance notes mainly deals with the in-depth analysis of electromagnetic phenomena when they are not performing any movements. Additionally, it is divided into ten further sub-topics to study the companion processes of reaching the state. These are - 1. Electric charge In this section of Physics ch 2 Class 12 notes, you get to learn about the basic features of electric charge and its expression in Physics. Along with its basics, the sections help to understand the full potential of charge. Different aspects of Charge included in Class 12 Physics Chapter 2 notes are - Definition Type: Positive and Negative Charge Unit and dimensional formula Point Charge Properties of Charge Comparison of Charge and Mass Methods of Charging Electroscope 2. Coulomb's Law Force is created when charges of opposite signs attract each other, and they repulse if the signs are the same. Coulomb's law tries to define this phenomenon through a mathematical formula, explicitly mentioned in Physics Class 12 notes Chapter 2. Moreover, there is key information about the variation of the constant k and its effect on a medium. Coulomb's law's vector form and the principle of superimposition are also explained in ch 2 Physics Class 12 notes. (Image will be uploaded soon) 3. Electric Field As stated in Class 12 Physics Chapter 2 notes, every positively or negatively charged particle has their respective electric fields. It feels a force at the time of interaction which might be attraction or repulsion. As it arises from electric charge, it is crucial to know about its different parts like - Electric field intensity Relation between electric force and electric field Super imposition of electric field Point charge Continuous charge distributions Properties of Electric Field Lines Motion of Charged Particles in an Electric field Learning more about the electric field from electric potential and capacitance notes Class 12 helps a student to get a grasp of upcoming chapters. 4. Electric Potential Energy When energy helps a charge to move from an electric field, it is known as the Electric Potential Energy. This section of electrostatic chapter Class 12 notes requires a student to study the Electron volt (eV), and the potential energy that an n number of charges can hold. 5. Electric Potential This section of Class 12 Physics Chapter 2 notes focuses on in-depth learning of Electric Potential or Voltage. Basically, it defines the potential movement of energy. 6. Relation between Electric Field and Potential Apart from knowing more about the relationship between the two values, Physics Class 12 Chapter 2 notes also discuss equipotential surfaces. 7. Electric Dipole Essentially, 'Dipoles' are two opposite points of charge represented with q and –q, with their distance between each other being 2a. Electric Dipoles are crucial in your study of Physics Class 12 Chapter 2 notes to learn more about electric fields and their potential. Additionally, Class 12 Physics Chapter 2 notes focus on the influence of electric dipoles on a uniform electric field mainly through Force and Torque, Work, and Potential Energy. In the last part of Electrostatics, further focus is on using the formulas to their fullest potential. It includes subsections of Electric Field, Electric Potential Energy, Electric Potential, and Electric Dipole. In the notes for electrostatic potential and capacitance, you will find proper solutions accompanied by clear and crisp diagrams for better understanding. 8. Gauss's Law Apart from just discussing the Gauss's Law, in Physics Class 12 ch 2 notes there is a thorough explanation of its properties and applications. The Gauss' Law states that net electric flux passing through a hypothetical closed surface is equal to the net electric charge present within the same closed surface. Being a broad part of the whole chapter, you may need to spend a little more time on it. Moving forward, it starts discussing the properties of conductors in relation to Gauss's Law. The Class 12 Physics notes Chapter 2 perfectly defines the journey to Gauss' Law from Coulomb's Law. Here is the Gauss's Law present in the Class 12 Physics ch 2 notes, (image will be uploaded soon) 9. Capacitors There is a dedicated section about Capacitors in the Class 12 Physics Chapter 2 notes elucidating its functions and importance as storage of potential electric energy. After explaining the structure of a capacitor, it points out the different types, parallel plate, spherical and cylindrical. The section of Chapter 2 notes of Physics Class 12 is further divided into subheads like: Properties of an ideal battery Grouping of capacitors Simple circuits (Series and Parallel) Dielectric Van de Graaff generator Combination of drops Charge distribution method Wheatstone Bridge-based circuit Extended Wheatstone Bridge Infinite network of capacitors Redistribution of charge between two capacitors Vedantu prepares the Class 12 Physics Chapter 2 notes with help from subject matter experts. In the PDF, you get a comprehensive idea of the topic along with potential answers to the most asked questions. Furthermore, the detailed explanation on each section and subsections are written in a simple language allows a student to ace their exams with wholesome knowledge. These Physics Chapter 2 Class 12 notes are going to be one of the best supplementary study materials besides a student’s textbooks. Visit the Vedantu website or download the app to get your hands on all important notes! Important Questions A charge of 4 × 10–8C is uniformly distributed on the surface of a spherical conductor, having a radius of 15 cm. Determine the electric field just outside this sphere at a point that is 15 cm from the centre of this sphere. Determine the capacitance given that the distance between the two plates has been reduced by half and the parallel plate capacitor holds a capacitance of 20 pF (where 1pF = 10-12 F) having air between the two plates. What will be the total capacitance of a combination where three capacitors, each having a capacitance of 20 pF, are connected in series. A square having a side of 10 cm has a 500 µC charge at its centre. Determine the work done to move a charge of 10 µC between two points that are diagonally opposite each other on the square. At an equatorial point, what will be the electrostatic potential because of an electric dipole? Calculate the work done to move a test charge, q, through a length of 1 cm along the equatorial axis of an electric dipole? Polarisation A capacitor has its plates enclosed in a medium that can be filled by insulating substances. A net dipole moment is then induced by an electric field in the dielectric. This event causes the field in an opposite direction. Equipotential Surface An equipotential surface is a type of surface where the potential always has a constant value. If considered as a point charge, the concentric spheres that are centred at a particular area of this charge are basically equipotential surfaces. Advantages of Vedantu's Revision Notes: A Comprehensive Resource for Effective Learning There are several reasons why one may refer to Vedantu's revision notes for studying a subject like Electrostatic Potential and Capacitance. Here are some key points: Comprehensive Coverage: Vedantu's revision notes provide a comprehensive coverage of the entire topic, ensuring that all important concepts and subtopics are included. Concise and Organized: The notes are designed to be concise, focusing on the key points and core ideas. They are organized in a structured manner, making it easy for students to navigate and revise the content. Simplified Explanation: The revision notes offer simplified explanations of complex concepts, making them more accessible and easier to understand. This helps students grasp the material more effectively. Key Formulas and Equations: The notes highlight the key formulas and equations relevant to the topic, ensuring that students have a clear understanding of the mathematical aspects of Electrostatic Potential and Capacitance. Examples and Illustrations: Vedantu's revision notes often include examples and illustrations that help clarify concepts and provide practical applications, enabling students to better relate theory to real-world scenarios. Quick Recap: The revision notes serve as a quick recap of the important points, allowing students to review the material efficiently before exams or assessments. Exam-Oriented Approach: Vedantu's revision notes are designed with an exam-oriented approach, focusing on the topics and concepts that are frequently asked in examinations. This helps students prepare effectively and increase their chances of scoring well. Accessible Anytime: Vedantu's revision notes are easily accessible online, allowing students to study at their convenience and revise the material anytime, anywhere.

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

Many of water’s biological functions stem from its chemical struc- ture. Recall that in the water molecule, H2O, the hydrogen and oxygen atoms share electrons to form covalent bonds. However, these atoms do not share the electrons equally. The oxygen atom has a greater ability to attract electrons to it because it pulls hydrogen’s electrons towards its nucleus. As a result, as shown in Figure 2-8, the region of the molecule where the oxygen atom is located has a partial negative charge, denoted with a , while the regions of the molecule where each of the two hydrogen atoms are located have partial positive charges, each of which are denoted with a . Thus, even though the total charge on a water molecule is neutral, the charge is unevenly distributed across the water molecule. Because of this uneven distribution of charge, water is called a polar compound. Notice also in Figure 2-8 that the three atoms in a water mole- cule are not arranged in a straight line as you might expect. Rather, the two hydrogen atoms bond with the single oxygen atom at an angle. SECTION 3 OBJECTIVES ● Describe the structure of a water molecule. ● Explain how water’s polar nature affects its ability to dissolve substances. ● Outline the relationship between hydrogen bonding and the different properties of water. ● Identify the roles of solutes and solvents in solutions. ● Differentiate between acids and bases. VOCABULARY polar hydrogen bond cohesion adhesion capillarity solution solute solvent concentration saturated solution aqueous solution hydroxide ion hydronium ion acid base pH scale buffer Copyright © by Holt, Rinehart and Winston. All rights reserved. (a) Electron cloud model (b) Space-filling model H H O The oxygen region of the water molecule is weakly negative, and the hydrogen regions are weakly positive. Notice the different ways to represent water, H2O. You are familiar with the electron cloud model (a). The space- filling model (b) shows the three- dimensional structure of a molecule. FIGURE 2-8 40 CHAPTER 2 Hydrogen bond H H H H H H H H H O O O O O O H H H H H – – – – – – – + + + + + + + + + + + + + + The dotted lines in this figure represent hydrogen bonds. A hydrogen bond is a force of attraction between a hydrogen atom in one molecule and a negatively charged region or atom in a second molecule. FIGURE 2-10 The positive region of a water molecule attracts the negative region of an ionic compound, such as the Cl portion of NaCl. Similarly, the negative region of the water molecule attracts the positive region of the compound—the Na portion of NaCl. As a result, NaCl breaks apart, or dissolves, in water. FIGURE 2-9 CI– Na+ H2O + + – – Solubility of Water The polar nature of water allows it to dissolve polar substances, such as sugars, ionic compounds, and some proteins. Water does not dissolve nonpolar substances, such as oil because a weaker attraction exists between polar and nonpolar molecules than between two polar molecules. Figure 2-9 shows how water dissolves the ionic compound sodium chloride, NaCl. In your body, ions, such as sodium and chloride, are essential to bodily func- tions, such as muscle contraction and transmission of impulses in the nervous system. In fact, dissolved, or dissociated ions, are pre- sent in all of the aqueous solutions found in living things and are important in maintaining normal body functions. HYDROGEN BONDING The polar nature of water also causes water molecules to be attracted to one another. As is shown in Figure 2-10, the positively charged region of one water molecule is attracted to the negatively charged region of another water molecule. This attraction is called a hydrogen bond. A hydrogen bond is the force of attraction between a hydrogen molecule with a partial positive charge and another atom or molecule with a partial or full negative charge. Hydrogen bonds in water exert an attractive force strong enough so that water “clings” to itself and some other substances. Hydrogen bonds form, break, and reform with great frequency. However, at any one time, a great number of water molecules are bonded together. The number of hydrogen bonds that exist depends on the state that water is in. If water is in its solid state all its water molecules are hydrogen bonded and do not break. As water liquifies, more hydrogen bonds are broken than are formed, until an equal number of bonds are formed and broken. Hydrogen bonding accounts for the unique properties of water, some of which we will examine further. These properties include cohesion and adhesion, the ability of water to absorb a relatively large amount of energy as heat, the ability of water to cool surfaces through evaporation, the density of ice, and the ability of water to dissolve many substances.

Why and How Managers Plan Importance of planning The planing process Benefits of planning Planning and time management Types of PLans used by managers Long term and short term plans Strageic and tactical plans Operational plans Planning Tools and Techiqunes Forecasting Contrigency planning Scenario planning Benchmaking Use of staff planners Implementing Plans to Achive Results Goal setting Goal management Goal alignment Participation and involvement Planning Def: The process of setting objectives and determining how best to accomplish them Planning at Eaton Corporation “Making the hard decision before events force them upon you, an anticipating the future needs of the market before the demand asset itself Objectives and goals Identifity the specific results or desired outcomes that one intends to achieve Plan Def: A statement of action steps to be taken in order to accomplish the objectives (goals) Steps in the planning process: Define your objectives Determine where you stand vis-a-vis objectives Develpo premises reagrdsing future conditions Analyze alternatives and make a plan Implement the plan and evaluate results What are the benefits of planning Improves focus and flexibility Imporves action orteitation Imporves coordination and control Imporves time management Time Managment Personal time management tips Do say “no” to request that distract you form what you should be doing Dont get bogged down inn details that can be addressed later Do screen telephone calls, emails and meeting request Dont let drop in visitors, text messaging use up your time Do prioritize your important and urgent work Dont become calendar bound by letting other control your schedule Do follow priorities; do most important and urgent work first Some 77% of mangers in one survey said that digital age has increased th number of decisions they have to make 43% said there was less time available to make these decisions Types of plans used by Managers What is teh time horizon Long term vs Short term Long term Look three or more years into teh future Short term plans Typically cover one year or less However: the increasing environmental complexity and dynamism of recent years has severely tested the concept of “long-term” planning Plans are subject to frequent revisions Most executives would likely agree that these complexities adn uncertainties challenge how er actually go about planning and how far ahead we can really plan At the very least we can conclude that there is a lot less permanency to long term plans today and that tey are subject to frequent revision Managment reaeracher Eillot Jaques believes tha people vary in their capability to think with different time horizons Types of Plans used by Managers (3 of 5) Strategic plans Set broad, comprehensive and linger term action directions for teh entire organization or major division Vision Clarifies purpose of the organization and what it hopes to be on the future Typical plans Specify how the organizations resources are used to implement strategy Tactical plans in business often take the form of functional plans Functional plans Incidate how different component within the organiztion will help accompnlish the overall strategy Production plans Finacial plans Facilites Plans Logisitc plans Marketing plans Human Resource Plans Operation plans Describe short-term activities to implement strategic plans Policies: Are standing plans that communicate guidelines for decisions Ex: Policies on office romances: The media is quick to report when a top executive or public figures runs into trouble over an office affair. Are there ant policies on office romances? Employer polices on office raltioshiis vary. One survey find teh following: 24% prohibit relationships among employees in the same department 13% prohibit relationships among employees who have the smae supervisor 80% prohibit relationships between supervisors and subordinates 5% have no restrictions on office romances Procedures: Are rules that describe actions to be taken in specific situations Budgets: are single use plans that commit resources to projects or activities Zero based budgets: allocate resources as if each budget were brand new There is no guarantee that any past funding will be renwer. All propsales, old and new, must compete for available funds at teh start of each new budget cycle Forcasting Attempts to predict the future Qualitaive forecasting uses expert opinions Quantitative forecasting uses mathematical models and statiscal aanylsis of historical data dna surveys Contingency planning Identify alternative course of action to take when things go wrong Anticipate changing conditions Contain trigger points to indicate when to activate plan (or a specific course of action) Scenario planning A long term version of contingency planning Identifying alternative future scenarios Plans made for each future scenario Increases organizations flexibility and preparation for future shocks Benchmarking Use of external and internal comparisons to better evaluate current performance Adopting best practices: things people adn organization do that lead to superior performance Staff Planners Experts who assist in all steps of the planning process They help bring focus and expertise to a wide variety of planning tasks Important: Communication between staff planers landline managers is essential for teh success of teh planning process Goal Setting - Always set SMART goal The solution: Goal Aligment Between Team Leader and Team Member Jonintly plan: Set objectives, set standards, choose actions Individually acy: Perform tasks (member), provide support (leader) Jointly control: Review results, discuss implications, renew cycle x4 Collective effort and commitment Participatroy planning Includes in all planning steps that people who will be affected by the plans adn askedd to help implement them Unloacks motivational potential of goal setting Management by objective (MBO) promotes participation Participation increases understanding and acceptance of plan and commitment to success Participatory planning - Number of people involved in teh decision making process Amazon is intensely focused on what it does. It believes in creating tight single-threaded teams, also known as “2 pizza team.” Data and Decision Making What are some of the important competencies managers must have today? Delegate Marketing and technology Manager must have Technological competency Ability to understand new technologies and to use them to their best advantage Information competency Ability to locate, gather, organize and display information for decision-making and problem solving Analytical competency Ability to evaluate and analyze information to make actual decisions and solve real problems What is the difference between Data and Information Data Raw facts and observation Information Data made useful and meaningful for decision-making Important concepts Big data Exists in huge quantities and is difficult to process without sophisticated mathematical and analytical techniques Data production today Bernard Marr is an internationally best-selling author. He helps organizations improve their business performance, use data more intelligently Data mining The process of analyzing data to produce useful information for decision-makers Management Analytics The systematic evaluation and analysis of data to make informed decision Information drives management Bad Data Refers to information that can be erroneous, misleading, and without general formatting The challenge: Can er use the data that is available in the “Big Data” Needs to be valid Can not trust everything out there Being ethical Look at the trends Data is structured and unstructured Data BIg Data = Structured + Unstructured Information Drive Management decision making What are the characteristics of useful information Easy to access If its credible Accurate Characteristics of useful information: Timely High quality Complete Relevant Understandable What about bad data It's not credible Miss information If it is not structured/ organized Bias based on opinions Confusing If its updated Bad data Refers to information that can be erroneous miss What are some examples of Management information system Business intelligence -BI Information systems to extract and report data in organized ways that are useful to decision-makers Executive dashboards Visually update and display key performance metrics (or Key Performance Indicators -KPIs) and information on a real-time basis Information needs in organization External Environment Information exchanges with the external environment Gather intelligence information Provide public information Information needs within the organizations (internal Enviroement) Information exchange within the organization Facilitate decision making Facilitate problem-solving Managers as information processors Continually gather, share and receive information Now as much electronic as it is face-to-face Always on, always connected How many people telecommute at least once a week 70% of people globally work remotely at least once a week, Work at home after covid 19 our forecast Our best estimate it that 25-30% of the workforce will be working form home multiple days a week by the end of 2021 As of 2023, 12.7% of full time employees work from home, while 28.2% work a hybrid model Managers as problem solvers Problem-solving The process of identifying a discrepancy between actual and desired performance and taking action to resolve it Ishikawa Fishbone diagram To identify the cause of problems Decision A choice among possible alternative courses of action Performance threat Something is wrong or has the potential to go wrong Performance opportunity The situation offers the chance for a better future if the right steps are taken Problem-solving approaches or style - from textbook Problem avoiders Inactive in information gathering and solving problems Problem seekers Proactive in anticipation of problems and opportunities and taking appropriate action to gain an advantage Problem solvers Reactive in gathering information and solving problem Managers - can approach problems in a systematic or intuitive manner Systematic thinking approaches problem in rational, step-by-step and analytical fashion Intuitive thinking approaches problems in a flexible and spontaneous fashion Multidimensional thinking- applies both intuitive and systematic thinking Managers face structured and unstructured problems Structure problems Are ones that are familiar, straight forward, and clear with respect to information needs Program decisions apply solutions that are readily available from past experiences to solve structured problems Know how to solve them Familiar Know what we are dealing with Unstructured problems Are ones that are full of ambiguities and information deficiencies Nonprogrammed decisions apply a specific solution to meet the demands of a unique problem Commonly faced by higher-level management Crisis decision making A crisis involves an unexpected problem that can lead to disaster if not resolved quickly and appropriately Ruled for crisis management Figure out what is going on Remember that speed matters Remember that slow counts, too Respect the danger of the unfamiliar Value the skeptic Be ready to “fight fire with fire” Managers make decisions with various amounts of information Certain environment Offers complete information on possible action alternatives and their consequences Risk environment Lacks complete information but offers probabilities of the likely outcomes for possible action alternatives Uncertain environment Lacks so much information that it is difficult to assign probabilities to the likely outcomes of alternative Ex: Certain and uncertain environments: The worldwide Governance Indicators for over 200 countries, comparing distinct environments (Canada-Brazil) Step 1-Identify and define the problem Focuses on information gathering information processing and deliberation Decision objectives should be established What are some common mistakes in definding problems? Common mistakes in defining problems Defining the problem too broadly or too narrowly Focusing on symptoms instead of causes Choosing the wrong problem to deal with Step 2- Generate and Evaluate Alternative Courses of Action Potential solutions are formulated and more information is gathered, data are analyzed, the advantages and disadvantages of alternative solutions are identified Common mistakes: Abandoning the search for alternatives too quickly Step 3- Decide on a preferred course of Action Two different approaches Behavioural model leads to satisficing decisions Classical model les to optimising decisions Behavioural Model Rationality is bounded because: There are limits our thinks capacity Available information (incomplete) Time constraints Step 4-Implement the decision Involves taking action to make sure the solution decided upon becomes a reality Managers need to have the willingness and ability to implement action plans Problems: Lack of participation error should be avoided Step 5 - Evaluate Results Involves comparing actual and desired results The positive and negative consequences of the chosen course of action should be examined If actual results fall short desire results, the manager returns to earlier steps in the decision-making process At all steps, check ethical reasoning Ask these spotlight questions Utility Does teh decision satisfy all constituents or stakeholders Rights Does the description respect the rights and duties of everyone? Justice Is the decision consistent with the canons of justice Caring Is the decision consistent with my responsibilities to care? Issues in decision-making How do errors happen? Heuristics: are strategies for simplifying decision-making Availability Bias: Bases a decision on recent information or events Representativeness bias: Bases a decision on similarity to other situations Anchoring and Adjustment Bias: Bases a decision on incremental adjustment from a prior decision point Framing error: Tring to solve a problem in the context perceived, positive or negative Confirmation Error: Focusing on information that confirms a decision already made Escalating commitment: Continuing a course of action even though it is not working Creative Decision making Creativity is the generation of a novel idea or unique approach that solves a problem or crafts an opportunity Big C: Creativity occurs when extraordinary things are done by exceptional people Little C: Creativity occurs when average people come up with unique ways to deal with daily events and situations The three types of situational creativity drivers Chapter review What are objectives and goals? The specific results or desired outcomes What are the 5 characteristics of great (SMART) goals? Forecasting - Attempts Qualitative forecasting uses options Quantitative forecasting uses mathematical models and statistical analysis of historical data and surveys Scenarios-Oracle’s crystal ball combines qualitative and quantitative methods

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