What was a major weakness of the Articles of Confederation?

The federal government could not collect taxes

It allowed for direct elections

What was one major accomplishment of the Articles of Confederation?

The creation of a national bank

The drafting of the Bill of Rights

The establishment of a standing army

Which document replaced the Articles of Confederation?

The Declaration of Independence

What was the primary reason the Articles of Confederation were replaced?

They created a weak central government

They established a strong military

They encouraged international trade

Which event highlighted the weaknesses of the Articles of Confederation?

The signing of the Declaration of Independence

What significant issue did the Three-Fifths Compromise address at the Constitutional Convention?

Representation of slaves in Congress

What was the main purpose of the Constitutional Convention held in 1787?

To address the weaknesses of the Articles of Confederation

To create a new political party

To draft the Declaration of Independence

What was a major outcome of the Constitutional Convention of 1787?

The creation of the United States Constitution

The declaration of independence

What was the purpose of the Federalist Papers?

To promote the ratification of the U.S. Constitution

To criticize the Articles of Confederation

To write the Declaration of Independence

What did Federalists believe was necessary for a stable government?

Direct democracy without a representative government.

What was a major concern for the Anti-Federalists regarding the Constitution?

The establishment of a national bank.

The requirement of a standing army.

The power of the Supreme Court.

What fear did the Anti-Federalists have regarding the proposed Constitution?

It would limit the power of individual states.

It would abolish the presidency.

It would create a stronger Bill of Rights.

It would promote economic equality.

Who were some of the prominent leaders associated with the Federalist movement?

Alexander Hamilton and James Madison

John Adams and Benjamin Franklin

Thomas Jefferson and Patrick Henry

What was the main argument of Federalists regarding the Constitution?

It provided a system of checks and balances

It limited the power of the states

Seven principles of the constitution

Democratic Constitution in South Africa Struggle against Apartheid • Apartheid was the name of a system of racial discrimination unique to South Africa. • This system was particularly oppressive for the blacks. → They were forbidden from living in white areas. • Since 1950, the blacks, coloured and Indians fought against the apartheid system. • The African National Congress (ANC) was the umbrella organisation that led the struggle against the policies of segregation. • In 1964, Nelson Mandela and seven other leaders were sentenced to life imprisonment in 1964 for daring to oppose the apartheid regime in his country. Towards a New Constitution • As protests and struggles against apartheid had increased, the white regime changed its policies. • After 28 years of imprisonment, Nelson Mandela released from jail. • At the midnight of 26 April 1994, democracy was adopted as a form of government in South Africa. • After two years, a constitution came out which gave to its citizens the most extensive rights available in any country. Why do we need a Constitution? • A constitution is necessary because: → It generates a degree of trust and coordination that is necessary for different kind of people to live together. → It specifies how the government will be constituted, who will have power to take which decisions. → It lays down limits on the powers of the government and tells us what the rights of the citizens are. → It expresses the aspirations of the people about creating a good society. Making of the Indian Constitution • In 1928, Motilal Nehru and eight other Congress leaders drafted a constitution for India. • In 1931, the resolution at the Karachi session of the Indian National Congress dwelt on how independent India’s constitution should look like. • Factors contributed to the making of our Constitution. → Ideals of French Revolution → The practice of parliamentary democracy in Britain → The Bill of Rights in the US → The socialist revolution in Russia The Constituent Assembly • In July 1946, Elections to the Constituent Assembly were held. → The drafting of the document called the constitution was done Constituent Assembly. → Dr. Rajendra Prasad was the Chairman of the Constituent Assembly. → In December 1946, the first meeting was held. • After the country was divided into India and Pakistan, the Constituent Assembly also got divided. • The Assembly adopted the Constitution on 26 November 1949 but it came into effect on 26 January 1950. • To mark this day we celebrate January 26 as Republic Day every year. • The Constituent Assembly worked in a systematic, open and consensual manner. → First some basic principles were decided and agreed upon. → Then a Drafting Committee chaired by Dr. B.R. Ambedkar prepared a draft constitution for discussion. → More than two thousand amendments were considered. Philosophy of the Constitution • The Constitution begins with a short statement of its basic values which is called the Preamble to the constitution. The preamble focuses on: → Justice, social, economic and political. → Liberty of thoughts, expression, belief, faith and worship. → Equality of status and of opportunity. → Fraternity assuring the dignity of the individual and the unity and integrity of the nation.

The Principles of the Constitution (1-5)

Can you make a multiple choice of test questions regarding this information given which is Curriculum from Different Points of View There are many definitions of curriculum. Because of this, the concept of curriculum is sometimes characterized as fragmentary, elusive and confusing. However, the numerous definitions indicate dynamism that connotes diverse interpretations of what curriculum is all about. The definitions are influenced by models of thought, pedagogies, political as well as cultural experiences. Let us study some of these definitions. 1. Traditional Points of View of Curriculum In early years of the 20th century, the traditional concepts held of the “curriculum is that it is a body of subjects or subject matter prepaid by the teachers for the student’s to learn”. It was synonymous to the “course of study” and “syllabus” Robert M. Hutchins views curriculum as “permanent studies” where the rules of grammar, reading, rhetoric and logic and mathematics for basic education are emphasized. Basic education should emphasize the 3 Rs and college education should be grounded on liberal education. On the other, Arthur Bestor as an essentialist, believes that the mission of the school should be intellectual training, hence curriculum should focus on the fundamental intellectual disciplines of grammar, literature and writing. It should also include mathematics, science, history and foreign language. The definition leads us to the view of Joseph Schwab that discipline is the sole source of curriculum. Thus in our education system, curriculum is divided into chunks of knowledge we call subject areas in basic education such as English, Mathematics, Science, Social Studies and others. In college, discipline may include humanities, sciences, language and many more. To Phoenix, curriculum should consist entirely of knowledge which comes from various disciplines. Academic discipline became the view of what curriculum is after the cold war and the race to space. Joseph Schwab, a leading curriculum theorist coined the term discipline as a ruling doctrine for curriculum development. Curriculum should consist only of knowledge which comes from disciplines which is the sole source. Thus curriculum can be viewed as a field of study. It is made up of its foundations (philosophical, historical, psychological and social foundations); domains of knowledge as well as its research theories and principles. Curriculum is taken as scholarly and theoretical. It is concerned with broad historical, philosophical and social issues and academics. Most of the traditional ideas view curriculum as written documents or a plan of action in accomplishing goals. 2. Progressive Points of View of Curriculum On the other hand, to a progressivist, a listing of school subjects, syllabi, course of study, and a list of courses or specific discipline do not make a curriculum. These can only be called curriculum if the written materials are actualized by the learner. Broadly speaking, curriculum is defined as the total learning experiences of the individual. This definition is anchored on John Dewey’s definition of experience and education. He believed that reflective thinking is a means that unifies curricular elements. Thought is not derived from action but tested by application. Caswell and Campbell viewed curriculum as “all experiences children have under the guidance of teachers”. This definition is shared by Smith, Stanley and Shores when they defined “curriculum as a sequence of potential experiences set up in the schools for the purpose of disciplining children and youth in group ways of thinking and acting”. Marsh and Willis on the other hand view curriculum as all the “experiences in the classroom which are planned and enacted by the teacher, and also learned by the students”. Points of View on Curriculum Development From the various definitions and concepts presented, it is clear that curriculum is a dynamic process. Development connotes changes which are systematic. A change for the better means any alteration, modification or improvement of existing condition. To produce positive changes, development should be purposeful, planned and progressive. This is how curriculum evolves. Let us look at the two models of curriculum development and concepts of Ralph Tyler and Hilda Taba. Ralph Tyler Model: Four Basic Principles. This is also popularly known as Tyler’s Rationale. He posited four fundamental questions or principles in examining any curriculum in schools. These four fundamental principles are as follows: 1. What educational purposes should the school seek to attain? 2. What educational experiences can be provided that are likely to attain these purposes? 3. How can these educational experiences be effectively organized? 4. How can we determine whether these purposes are being attained or not? In summary, Tyler’s Model show that in curriculum development, the following considerations should be made: (1) Purpose of the school, (2) Educational experiences related to the purposes, (3) Organization of the experiences, and (4) Evaluation of the experiences. On the other hand, Hilda Taba improved on Tyler’s Rationale by making a linear model. She believed that teachers who teach or implement the curriculum should participate in developing it. Her advocacy was commonly called the grassroots approach. She presented seven major steps to her model where teachers could have a major input. These steps are as follows: 1. Diagnosis of learner’s needs and expectations of the larger society. 2. Formulation of learning objectives. 3. Selection of learning content. 4. Organization of learning content. 5. Selection of learning experiences. 6. Organization of learning activities. 7. Determination of what to evaluate and the means of doing it. Thus as you look into curriculum models, the three interacting processes in curriculum development are planning, implementing and evaluating. Types of Curriculum Operating in Schools From the various concepts given, Allan Glatthorn(2000) describes seven types of curriculum operating in the schools. These are (1) Recommended curriculum- proposed by scholars and professional organizations. (2) Written Curriculum- appears in school, district, division or country documents. (3) Taught Curriculum- what teacher’s implement or deliver in the classrooms and schools. (4) Supported Curriculum- resources-textbooks, computers, audio- visual materials which support and help in the implementation of the curriculum. (5) Assessed Curriculum- that which is tested and evaluated. (6) Learned Curriculum- which the students actually learn and what is measured and (7) Hidden Curriculum- the unintended curriculum. 1. Recommended Curriculum- Most of the school curricula are recommended. The curriculum may come from a national agency like the Department of Education, Commission on Higher Education (CHED), Department of Science and Technology (DOST) or any professional organization who has stake in education. For example the Philippine Association for Teacher Education (PAFTE) or the Biology Teacher Association (BIOTA) may recommend a curriculum to be implemented in the elementary or secondary education. 2. Written Curriculum- This includes documents, course of study or syllabi handed down to the schools, districts, division, departments or colleges for implementation. Most of the written curricula are made by curriculum experts with participation of teachers. These were pilot-tested or tried out in sample schools or population. Example of this is the Basic Education Curriculum (BEC). Another example is the written lesson plan of each classroom teacher made up of objectives and planned activities of the teacher. 3. Taught Curriculum- The different planned activities which are put into action in the classroom compose the taught curriculum. These are varied activities that are implemented in order to arrive at the objectives or purposes of the written curriculum. These are used by the learners with the guidance of teachers. Taught curriculum varies according to the learning styles of students and the teaching styles of teachers. 4. Supported Curriculum- In order to have a successful teaching, other than the teacher, there must be materials which should support or help in the implementation of a written curriculum. These refer to the support curriculum that includes material resources such as textbooks, computers, audio-visual materials, laboratory equipment, playgrounds, zoos and other facilities. Support curriculum should enable each learner to achieve real and lifelong learning. 5. Assessed Curriculum- This refers to a tested or evaluated curriculum. At the duration and end of the teaching episodes, series of evaluations are being done by the teachers to determine the extent of teaching or to tell if the students are progressing. This refers to the assessed curriculum. Assessment tools like pencil-and-paper tests, authentic instruments like portfolio are being utilized. 6. Learned Curriculum- This refers the learning outcomes achieved by the students. Learning outcomes are indicated by the results of the tests and changes in behavior which can either be cognitive, affective or psychomotor. 7. Hidden Curriculum- This is the unintended curriculum which is not deliberately planned but may modify behavior or influenced learning outcomes. There are lots of hidden curricula that transpire in the schools. Peer influence, school environment, physical condition, teacher-learner interaction, mood of the teachers and many other factors made up the hidden curriculum.

Reading Passage: The Anatomy of a Kill Chain In the lexicon of modern warfare, the term "kill chain" describes the end-to-end process of a military attack, from the initial identification of a target to its eventual destruction and the subsequent evaluation of the strike's effectiveness. Conceptually, the kill chain is a structural model used to understand and optimize the speed and precision of military operations. The fundamental principle of this model is that an attack functions as a sequence of interdependent stages; if any single link in the chain is broken, the entire operation fails. For strategic planners, this creates a dual objective: to accelerate one's own kill chain while simultaneously finding ways to disrupt the adversary's. Strategic Concept: The Kinetic Model (F2T2EA) The traditional military kill chain is often summarized by the acronym F2T2EA, representing a continuous cycle of find, fix, track, target, engage, and assess. The kinetic kill chain begins with Find, the reconnaissance phase where intelligence assets identify a potential target within a theater of operations. Once found, the process moves to Fix, which involves pinning down the target's specific location and ensuring it can be distinguished from friendly forces or non-combatants. Track follows, maintaining a persistent watch on the target's movements to prevent its escape. In the Target phase, commanders select the appropriate weapon system and verify the legality and strategic value of the strike. Engage is the kinetic moment—the actual deployment of ordnance against the objective. Finally, Assess involves battle damage assessment (BDA) to determine if the desired effects were achieved or if further engagement is required. This model emphasizes "compressing the sensor-to-shooter timeline," meaning the faster a military can move through these steps, the more lethal it becomes. The Evolution: The Cyber Kill Chain® As warfare expanded into the digital domain, Lockheed Martin adapted the kinetic model into the Cyber Kill Chain. This framework assists defenders in identifying and stopping Advanced Persistent Threats (APTs). Unlike a physical missile, a cyberattack often unfolds over weeks or months, but the sequential logic remains the same. The model consists of seven distinct stages: Stage Description of Attacker Activity 1. Reconnaissance The harvesting of information. Attackers research targets via social media, public records, and technical scanning to find vulnerabilities. 2. Weaponization Coupling a remote access trojan with an exploit into a deliverable payload (e.g., a malicious PDF or Microsoft Office document). 3. Delivery Transmission of the weapon to the target environment. Common vectors include email attachments, malicious websites, or USB drives. 4. Exploitation The weapon triggers. The code executes on the victim's system, typically by taking advantage of a software or operating system vulnerability. 5. Installation The attacker installs a persistent backdoor or malware on the victim's system, allowing them to maintain access even after a reboot. 6. Command & Control (C2) The compromised system opens a communication channel back to the attacker's server, allowing the intruder to give manual instructions. 7. Actions on Objective The final stage where the attacker achieves their goal, such as data exfiltration, encryption for ransom, or destruction of critical infrastructure. Strategic Implications for Defense The strategic value of the Cyber Kill Chain lies in its ability to provide a roadmap for "proactive defense." By understanding the sequence, security professionals can implement controls at every stage. For instance, robust email filtering can break the chain at the Delivery stage, while endpoint detection can stop the Installation phase. Crucially, the earlier a defender breaks the chain, the lower the cost of mitigation and the lower the risk of damage. If an attacker is stopped during Reconnaissance, they have gained nothing. If they are stopped during Actions on Objective, the damage may already be catastrophic. In both kinetic and cyber environments, the goal is the same: to create a "defensive depth" that makes the cost of a successful attack prohibitively high for the adversary.

All living things are made up of one or more cells. A cell is the smallest unit that can carry on all of the processes of life. Beginning in the 17th century, curious naturalists were able to use microscopes to study objects too small to be seen with the unaided eye. Their studies led them to propose the cellular basis of life. Hooke In 1665, English scientist Robert Hooke studied nature by using an early light microscope, such as the one in Figure 4-1a. A light micro- scope is an instrument that uses optical lenses to magnify objects by bending light rays. Hooke looked at a thin slice of cork from the bark of a cork oak tree. “I could exceedingly plainly perceive it to be all perforated and porous,” Hooke wrote. He described “a great many little boxes” that reminded him of the cubicles or “cells” where monks live. When Hooke focused his microscope on the cells of tree stems, roots, and ferns, he found that each had similar little boxes. The drawings that Hooke made of the cells he saw are shown in Figure 4-1b. The “little boxes” that Hooke observed were the remains of dead plant cells, such as the cork cells shown in Figure 4-1c. SECTION 1 OBJECTIVES ● Name the scientists who first observed living and nonliving cells. ● Summarize the research that led to the development of the cell theory. ● State the three principles of the cell theory. ● Explain why the cell is considered to be the basic unit of life. VOCABULARY cell cell theory Robert Hooke used an early microscope (a) to see cells in thin slices of cork. His drawings of what he saw (b) indicate that he had clearly observed the remains of cork cells (300) (c). FIGURE 4-1 (a) (b) (c) Copyright © by Holt, Rinehart and Winston. All rights reserved. 70 CHAPTER 4 Leeuwenhoek The first person to observe living cells was a Dutch trader named Anton van Leeuwenhoek. Leeuwenhoek made microscopes that were simple and tiny, but he ground lenses so precisely that the magnification was 10 times that of Hooke’s instruments. In 1673, Leeuwenhoek, shown in Figure 4-2a, was able to observe a previ- ously unseen world of microorganisms. He observed cells with green stripes from an alga of the genus Spirogyra, as shown in Figure 4-2b, and bell-shaped cells on stalks of a protist of the genus Vorticella, as shown in Figure 4-2c. Leeuwenhoek called these organisms animalcules. We now call them protists. THE CELL THEORY Although Hooke and Leeuwenhoek were the first to report observ- ing cells, the importance of this observation was not realized until about 150 years later. At this time, biologists began to organize information about cells into a unified understanding. In 1838, the German botanist Matthias Schleiden concluded that all plants were composed of cells. The next year, the German zoologist Theodor Schwann concluded the same thing for animals. And finally, in his study of human diseases, the German physician Rudolf Virchow (1821–1902) noted that all cells come from other cells. These three observations were combined to form a basic theory about the cel- lular nature of life. The cell theory has three essential parts, which are summarized in Table 4-1. Anton van Leeuwenhoek (1632–1723) is shown here with one of his hand-held lenses (a). Leeuwenhoek observed an alga of the genus Spirogyra (b) and a protist of the genus Vorticella (c). FIGURE 4-2 TABLE 4-1 The Cell Theory All living organisms are composed of one or more cells. Cells are the basic units of structure and function in an organism. Cells come only from the reproduction of existing cells. (a) (b) (c) www.scilinks.org Topic: Cell Theory Keyword: HM60241 mb06se_csfs01.qxd 5/18/07 10:54 AM Page 70

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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