Finding area and perimeter of squares and rectangles

Finding Area of Triangles, Squares, and Rectangles

Contact with the Americas In 1001, Viking sailors led by Leif Erikson reached the eastern tip of North America. Archaeologists have found evidence of the Viking settlement of Vinland in present-day Newfoundland, Canada. The Vikings did not stay in Vinland long and no one is sure why they left. However, Viking stories describe fierce battles with Skraelings, the Viking name for the Inuit. Evidence suggests that Asians continued to cross the Bering Sea into North America after the last ice age ended. Some scholars believe that ancient seafarers from Polynesia may have traveled to the Americas using their knowledge of the stars and winds. Modern Polynesians have sailed canoes thousands of miles in this way. Still others think that fishing boats from China and Japan blew off course and landed on the western coast of North or South America. Perhaps such voyages occurred. If so, they were long forgotten. Before 1492, the peoples of Asia and Europe had no knowledge of the Americas and their remarkable civilizations. The Voyages of Columbus Portuguese sailors had pioneered new routes around Africa toward Asia in the late 1400s. Spain, too, wanted a share of the riches. King Ferdinand and Queen Isabella hoped to keep their rival, Portugal, from controlling trade with India, China, and Japan. They agreed to finance a voyage of exploration by Christopher Columbus. Columbus, an Italian sea captain, planned to reach the East Indies by sailing west across the Atlantic. Finding a sea route straight to Asia would give the Spanish direct access to the silks, spices, and precious metals of Asia. The spice trade was a major cause for European exploration and a reason the Spanish rulers supported Columbus’s voyage. They also wanted wealth from any source. “Get gold,” King Ferdinand said to Columbus. “Humanely if possible, but at all hazards—get gold.” Crossing the Atlantic In August 1492, Columbus set out with three ships and about 90 sailors. As captain, he commanded the largest vessel, the Santa María. The other ships were the Niña and the Pinta. After a brief stop at the Canary Islands, the little fleet continued west into unknown seas. Fair winds sped them along, but a month passed without the sight of land. Some sailors began to grumble. They had never been away from land for so long and feared being lost at sea. Still, Columbus sailed on. On October 7, sailors saw flocks of birds flying southwest. Columbus changed course to follow the birds. A few days later, crew members spotted tree branches and flowers floating in the water. At 2 a.m. on October 12, the lookout on the Pinta spotted white cliffs shining in the moonlight. “Tierra! Tierra!” he shouted. “Land! Land!” At dawn, Columbus rowed ashore and planted the banner of Spain. He was convinced that he had reached the East Indies in Asia. He called the people he found there “Indians.” In fact, he had reached islands off the coasts of North America and South America in the Caribbean Sea. These islands later became known as the West Indies. For three months, Columbus explored the West Indies. To his delight, he found signs of gold on the islands. Eager to report his success, he returned to Spain. Columbus Claims Lands for Spain In Spain, Columbus presented Queen Isabella and King Ferdinand with gifts of pink pearls and brilliantly colored parrots. Columbus brought with him many things that Europeans had never seen before: tobacco, pineapples, and hammocks used for sleeping. Columbus also described the “Indians” he had met, the Taino (ty noh). The Taino, he promised, could easily be converted to Christianity and could also be used as slaves. The Spanish monarchs were impressed. They gave Columbus the title Admiral of the Ocean Sea. They also agreed to finance future voyages. The promise of great wealth, and the chance to spread Christianity, gave them a reason to explore further. Columbus made three more voyages across the Atlantic. In 1493, he founded the first Spanish colony in the Americas, Santo Domingo, on an island he called Hispaniola (present-day Haiti and the Dominican Republic). A colony is an area settled and ruled by the government of a distant land. Columbus also explored present-day Cuba and Jamaica. He sailed along the coasts of Central America and northern South America. He claimed all of these lands for Queen Isabella of Spain. Columbus proved to be a better explorer than governor. During his third expedition, settlers on Hispaniola complained of his harsh rule. Queen Isabella appointed an investigator, who sent Columbus back to Spain in chains. In the end, the queen pardoned Columbus, but he never regained the honors he had won earlier. He died in 1506, still convinced that he had reached Asia. The Impact of Columbus’s Voyages Columbus has long been honored as the bold sea captain who “discovered America.” Today, we recognize that American Indians had discovered and settled these lands long before 1492. We also recognize that Columbus and the Europeans who followed him treated the ancient inhabitants of the Americas brutally. Still, Columbus’s voyages did change history. They marked the beginning of lasting contact among the peoples of Europe, Africa, and the Americas. For a great many American Indians, contact had tragic results. Columbus and those who followed were convinced that European culture was superior to that of the Indians. The Spanish claimed Taino lands and forced the Taino to work in gold mines, on ranches, or in Spanish households. Many Taino died from harsh conditions or European diseases. The Taino population was wiped out. Still, the voyages of Columbus signaled a turning point for the Americas. A turning point is a moment in history that marks a decisive change. Curious Europeans saw the new lands as a place where they could settle, trade, and grow rich. Spanish Exploration Continues After the voyages of Columbus, the Spanish explored and settled other Caribbean islands that Columbus had found. They sought gold, land for crops, people to enslave, and converts to Christianity for the Spanish crown. By 1511, they had conquered Puerto Rico, Jamaica, and Cuba. They also explored the eastern coasts of North America and South America in search of a western route to Asia. In 1513, Vasco Núñez de Balboa (bal boh uh) crossed the Isthmus of Panama. American Indians had told him that a large body of water lay to the west. With a party of Spanish soldiers and Indians, Balboa reached the Pacific Ocean and claimed the ocean for Spain. The Spanish had no idea how wide the Pacific was until a sea captain named Ferdinand Magellan (muh jel un) sailed across it. The expedition—made up of five ships and about 250 crew members—left Spain in 1519. Fifteen months later, it cut through the stormy southern tip of South America by way of what is now known as the Strait of Magellan and entered the Pacific Ocean. Crossing the vast Pacific, the sailors ran out of food: Primary Source “We remained 3 months and 20 days without taking in provisions or other refreshments and ate only old biscuit reduced to powder, full of grubs and stinking from the dirt which rats had made on it. We drank water that was yellow and stinking.” —Antonio Pigafetta, The Diary of Antonio Pigafetta Magellan himself was killed in a battle with the local people of the Philippine Islands off the coast of Asia. In 1522, only one ship and 18 sailors returned to Spain. They were the first people to circumnavigate, or sail completely around, the world. In doing so, they had found an all-water western route to Asia. Europeans became aware of the true size of the Earth. How Did the Columbian Exchange Affect the Rest of the World? The encounter between the peoples of the Eastern and Western Hemispheres sparked a global exchange of goods and ideas. Because it started with the voyages of Columbus, this transfer is known as the Columbian Exchange. The Columbian Exchange refers to a biological and cultural exchange of animals, plants, human populations, diseases, food, government, technology, the arts, and languages. The exchange went in both directions. Europeans learned much from American Indians. At the same time, Europeans contributed in many ways to the culture of the Americas. This exchange also brought about many modifications, or changes, to the physical environment of the Americas, with both positive and negative results. Changing Environments Europeans introduced domestic animals such as chickens from Europe and Africa. European pigs, cattle, and horses often escaped into the wild and multiplied rapidly. Forests and grasslands were converted to pastures. As horses spread through what would become the United States, Indians learned to ride them and used them to carry heavy loads. Plants from Europe and Africa changed the way American Indians lived. The first bananas came from the Canary Islands. By 1520, one Spaniard reported that banana trees had spread “so greatly that it is marvelous to see the great abundance of them.” Oranges, lemons, and figs were also new to the Americas. In North America, explorers also brought such plants as bluegrass, the daisy, and the dandelion. These plants spread quickly in American soil and modified American grasslands. Tragically, Europeans also brought new diseases, such as smallpox and influenza. American Indians had no resistance to these diseases. Historians estimate that within 75 years, diseases from Europe had killed almost 90 percent of the people in the Caribbean Islands and in Mexico. American Indian Influences on Europe, Africa and Asia American Indians introduced Europeans to valuable food crops such as corn, potatoes, sweet potatoes, beans, tomatoes, manioc, squash, peanuts, pineapples, and blueberries. Today, almost half the world’s food crops come from plants that were first grown in the Americas. Europeans carried the new foods with them as they sailed around the world. Everywhere, people’s diets changed and populations increased. In South Asia, people used American hot peppers and chilies to spice stews. Chinese peasants began growing corn and sweet potatoes. Italians made sauces from tomatoes. People in West Africa grew manioc and corn. European settlers often adopted American Indian skills. In the North, Indians showed Europeans how to use snowshoes and trap beavers and other fur-bearing animals. European explorers learned how to paddle Indian canoes. Some leaders studied American Indian political structures. In the 1700s, Benjamin Franklin admired the Iroquois League and urged American colonists to unite in a similar way. Positive and Negative Consequences Through the Columbian Exchange, Europeans and American Indians modified their environments and gained new resources and skills. At the same time, warfare and disease killed many on both sides. Europeans viewed expansion positively. They gained great wealth, explored trade routes, and spread Christianity. Yet their farming, mining, and diseases took a toll on the physical environment and left many American Indians dead. Despite these negatives, the Columbian Exchange shaped the modern world, including what would become the United States.

Measuring the Effectiveness of police strategies and operations Clearance rates Def: The proportion of incidents known to the police that result in teh identification of a suspect Crime Displacement Def: relocation-due to the effective crime prevention, crime response initiates criminal activity from one local to another Professional Model of Policing Model of police work, reactive, incident driven and centred on random patrol Three Rs: random patrol, rapid response and reactive investigation Community policing Def: policing centred on police-community partnership and problem-solving The three ps: prevention, problem solving and partnership with the proactive role Community-based strategic policing Def: The model incorporates community policing with prevention, crime response and crime attack approaches Community engagement, police services strategic in their policies and operations Crime Analytics Sophisticated programs, and crime maps, provide intelligence to police officers in patrol and investigative units Intelligence-led policing: guided by collection, and analysis of information informs police decision-making Compstat: Increase effectiveness, and efficiency of police service while holding police personnel accountable for crime reduction Predictive policing: statistical analysis, identify time and location likely to occur Limited analytical capacity and not able to provide their officers with real-time information Biased policing certain areas, or persons, being identified as important for police attention in predictive policing How Predictive Policing Software Works The Police and the community Public Attitudes toward and Confidence in the police Community-based strategic policing: Recruitment, and deployment of volunteers in community police stations, storefronts Foot and bike patrols Team policing Restorative Justice Approaches Alternative for addressing, and resolving crime, needs of victims, offenders and the community Victim offender meditation Circle sentencing Community holistic healing programss Family group conferences Crime Prevention and Response Strategies Crime Prevention progemas Aimed at reducing crime, generating community involvement and heightening citizens; perceptions of safety Primary crime prevention programs opportunities for criminal offences and alter those conditions Secondary crime prevention programs focus on areas that produce crime and disorder Tertiary crime prevention programs are designed to prevent youth and adults from reoffending The Broken Windows Approach If minor crimes are left unaddressed in an environment, more serious crimes will emerge (originated in New York City in the 1980’s) “The exictsnce of unchecked and uncontrolled mirror incivilites in a neighbourhood- for example, panhandling, public drunkenness, vandalism and graffiti-produces an atmosphere conducive to more serious crime.” R.H. Burke Zero tolerance policing Zero tolerance policing: Strict order maintenance approach- specific area, coupled with high police visibility and presence Quality of life policing: Increased police visibility improves conditions in an area by targeting disruptive and annoying behaviour Problem Oritented policing (POP) Strategy, the idea that police should address teh cause of recurrent crime and disorder Root causes of recurring problems Solutions to problems Collabortaion with community SARA (scanning, analysis, response and assessment) problem-solving model helps officers identify, and respond to problems with the assistance of agencies, organizations, community groups The Police and Vulnerable/ At risk groups Persons with Mental Illness Patrol officers encountering more and more persons with mental illness (PwMi) Number of these end trragically Number of incidents increased significantly following deinstitutionalization of the mentally ill - in 1960 and 1970 De facto (in fact) mental health workers, first responders Crisis intervention training (CIT) Assertive outreach teams Assertive community treatment (ACT) teams Indigenouse, Vulnerable, and Marginalized women Sexual assault one of most underreported crimed. 1 in 20 incidents report to police. Many Women Do not want to deal with police Believe police would not take allegation seriously Language, cultural barriers Distrust the police Fear repercussions Missing and Murdered Indigenous women Canada, unknown number of missing and murdered indigenous women 2016, federal government announced National inquiry into Missing and Murdered Indigennouse women and girls Three goals of MMIWG 1. Finding the truth 2. Honouring the truth 3. Giving life to the truth as a path of healing

In a single domesticated grain seed, one might see the bud of great civilizations. The birth of agriculture was a turning point in humans' social development, as stable food supplies enabled people to transcend the constraints of food gained by hunting and gathering. After that, people were able to settle down and experience population booms. As one of the major areas around the globe where agriculture originated, China has contributed to the world's domesticated rice, millet, buckwheat and soybeans. Archaeological studies have unveiled that the planting of rice originated around 10,000 years ago in the lower reaches of the Yangtze River, leading to the eventual replacement there of hunting and gathering practices dating back 5,000 to 6,000 years. "It marked the formation of a rice-based agricultural society in the area," said Zhao Zhijun, an archaeologist at the Chinese Academy of Social Sciences. Archaeological studies of the origins of rice-based agriculture are an important part of a national project tracing the origins of Chinese civilization itself. President Xi Jinping has greatly valued the project. At a group study session of the Political Bureau of the Communist Party of China Central Committee on May 27, 2022, Xi, who is also general secretary of the CPC Central Committee, emphasized the significance of the project and the role that archaeological studies play in better understanding Chinese civilization. The project to trace the origins of Chinese civilization, in addition to finding signs of human activity more than 1 million years ago, has also proved that China's history includes 10,000 years of culture and more than 5,000 years of civilization. The project has provided clear knowledge of the origins and formation of Chinese civilization, the history of its development, the process of the formation and development of its pluralistic and integrated pattern, and the characteristics of the civilization and why it was formed in such a way, he added. This was not the first time that Xi emphasized the importance of the origin-tracing project. Since the 18th National Congress of the CPC in 2012, Xi has toured more than 100 historical and cultural locations and issued many instructions related to archaeology and the origin-tracing project. During the 23rd group study session of the Political Bureau of the CPC Central Committee in 2020, Xi called for giving more attention to archaeological research and letting historical facts speak for themselves. "This will provide strong support for our efforts to carry forward the best of traditional Chinese culture and increase our cultural confidence," said Xi. The origin-tracing project has been carried out since 2002. Its ongoing fifth phase, which started in 2020, involves the participation of more than 500 researchers from 29 institutes across the country. It primarily centers on several ancient capital sites, including the Liangzhu site in Hangzhou, Zhejiang province, the Taosi site in Xiangfen county, Shanxi province, the Shimao site in Shenmu, Shaanxi province, and the Erlitou site in Luoyang, Henan province, from 3,500 to 5,500 years ago, as well as other settlements mainly along the basins of the Yellow, Yangtze and Liaohe rivers. The project has also expanded to a wider geographic and chronological framework to decode how Chinese civilization emerged and how its diverse elements formed a unity. Excavation of the Liangzhu site, which is over 5,000 years old and is one of the major sites covered in the origin-tracing project, has yielded an inner city covering 3 million square meters and an outer city of 6.3 million sq m, making it the world's largest capital at the time. It also had a giant water control system, which contributed to the formation of a rice-based agricultural society. By calculating the earthwork volume, archaeologists found that building the entire ancient city, the water control system and Mojiaoshan — a 10-meter-tall man-made terrace in the center of the city — required 10,000 people working daily for seven-and-a-half years. The discoveries show that Liangzhu had a kingship able to organize people for large-scale public construction, and its social differentiation, emergence of the city concept and existence of a kingship prove that it became a civilized society, said Wang Wei, a veteran archaeologist at the Chinese Academy of Social Sciences. Significant topic Wang said that tracing the origins of a civilization is a significant topic in the research of human history. Over the years, the Chinese project has provided China's answer to how to define civilizations. In 2022, Xi commended the efforts and stressed that the project has made creative contributions to the research on tracing the origins of the world's civilizations. Wang said: "International academia has proposed three indispensable elements for a civilized society based on features of Mesopotamian and Egyptian civilizations: written characters, metallurgy and the city concept. But we can find that some of the three elements were absent in many ancient civilizations. For example, the Mayan civilization had no metallurgy, while the Incan civilization didn't have written characters." Western scholars believe that Chinese civilization began with the Yinxu Ruins in Anyang, Henan province, a capital of the late Shang Dynasty (c.16th century-11th century BC), based on the discovery of inscribed oracle bones from that time. However, Chinese archaeologists don't agree. With continued archaeological research, international academia now believes that places around the world can propose criteria for civilization based on their own ancient social development. China's archaeological studies have shaped the nation's criteria in defining a civilization: the development of productivity, an increase in population, the appearance of cities, social differentiation and the emergence of kingship and state. "These criteria are suitable for identifying other civilizations as well," said Wang. "Civilizations have in common the appearance of kingship and state. They are only different in the ways of imposing kingship and the forms of state." In China, kingship and state "were shown by exquisite jade and bronze ritual artifacts, grand palaces and magnificent mausoleums imitating aboveground palaces", he added. "In Mesopotamia and ancient Egypt, they were demonstrated through superb stone temples, pyramids and large-scale tombs." Multidisciplinary subject President Xi said in 2020 that archaeologists should work closely with researchers from other fields to make an interpretive analysis of material remains. Zhang Chi, a professor of archaeology at Peking University, said that since material remains are often the research focus of archaeological studies, these should not only be observed with the eyes, but also studied using scientific and technological tools. Therefore, from the perspective of research methods, archaeology is by nature a multidisciplinary subject, Zhang added.

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

There are 12 core values at BTS, with 4 core values being “non-negotiables”. Each of the 12 core values are categorized into 3 main groups, Permission to Play, Architect of the Future, and Guardian of the Mood, to further encapsulate the broader aspects of BTS's work culture. The 4 non-negotiables: Being Super Hungry: This value underscores an intrinsic motivation and a relentless pursuit of goals. It reflects an individual's aspiration to continually strive for success, always seeking opportunities to grow and excel. Strong Willingness to Learn: This value promotes a continuous desire for personal and professional growth. It represents an open-minded approach to acquiring new skills and knowledge, which is critical in the ever-evolving field of taxation and financial services. Burning Desire for an Abundant Lifestyle: This value aligns well with the firm's vision and mission. It showcases a passionate pursuit of a prosperous life, not just in terms of financial wealth but a comprehensive approach to abundance, involving personal well-being and satisfaction. Burning Desire to be the Best: This embodies the drive to excel and be at the forefront in one’s area of expertise. It encourages individuals to strive for excellence, setting the bar high and aiming to surpass it, fostering a culture of competitiveness and high performance. Permission to Play: This category delineates the foundational qualities BTS seeks in potential team members, reflecting a blend of passion, humility, presence, and aspiration for a prosperous life. Super Hungry: Being "Super Hungry" transcends personal ambition, creating an environment where passion and determination are contagious. It's about fostering an ecosystem of perpetual growth, where individuals are fervently working towards their goals while uplifting others. It represents a spirit of resilience and relentless forward motion, fostering a collective progress where success is a shared journey. Humble and Humility: Embracing humility is the cornerstone of personal and organizational growth at BTS. It encourages individuals to remain open to learning and receptive to constructive criticism, fostering a culture of continuous improvement. Humility embodies a willingness to relinquish ego, embracing the learnings that come through experiences and guidance. It cultivates a space where personal growth is accelerated through mutual respect and collaborative learning, ultimately paving the way for success. Burning Desire for an Abundant Lifestyle: This core value embodies a holistic pursuit of happiness, where individuals strive to find joy and fulfillment in various facets of life, including work, personal relationships, and mental well-being. It encourages a balanced approach to life, where passion for work aligns with personal joy, fostering a workplace where individuals are deeply committed and engaged in their roles, finding contentment and happiness in their professional pursuits. Being Fully Present and Inspiring: Being fully present encourages individuals to immerse themselves wholly in their tasks, minimizing distractions and maximizing productivity. It fosters a workplace where people are engaged, content, and genuinely invested in their roles. Simultaneously, nurturing an inspiring environment is about personal growth and self-motivation, where individuals are the driving forces behind their success, igniting inspiration through their journey and accomplishments, fostering a cycle of mutual motivation and growth. Architect of the Future: This category is about the cultivation of leaders within the team, encouraging qualities such as self-drive, innovation (revolutionist), a strong willingness to learn, and an unyielding desire to be the best in their field. Being Self-Driven: A self-driven individual embodies responsibility and initiative, equipped with a clear vision and a proactive approach to achieving their goals. They are fervent in bridging the gap between their present and envisioned future, fostering a goal-oriented mindset that is aggressive in its pursuit and focused on accomplishing its objectives. Being a Revolutionist: A revolutionist in the BTS context is an innovator, willing to defy conventional norms and embrace new approaches to foster growth and development. They are vocal advocates for change, bringing unique perspectives and solutions to the table, fostering an environment of innovation and progressive thinking. Even amidst resistance, they hold firm to their vision, aligning their actions with the core values and purpose that guide BTS's mission. Strong Willingness to Learn: An individual with a strong willingness to learn is adaptable, constantly evolving to meet the changing demands of the industry. They are voracious learners, continually seeking knowledge to enhance their expertise, thereby adding value to the clients and the organization. Burning Desire to be the Best: This value is about embodying excellence in every endeavor, fostering a culture where individuals are constantly striving to elevate their expertise and services. It encourages a proactive approach to personal and professional growth, where the quest for greatness is a continuous journey, propelled by learning and innovation. Guardian of the Mood: This focuses on maintaining a positive and collaborative work environment, emphasizing values such as gratefulness, patience, excitement, and helpfulness. It suggests that BTS values not only professional excellence but also emotional intelligence and positive interpersonal interactions. Being Grateful: Being grateful at BTS embodies a conscious appreciation of the opportunities and resources at hand. It encourages individuals to not just focus on personal milestones but to recognize and value the collective efforts and accomplishments of the team. It's about harboring a mindset of thankfulness that permeates everyday life, understanding that the privilege to progress and succeed is not to be taken for granted. This attitude fosters a nurturing environment where gratitude amplifies abundance, paving the way for more blessings and opportunities to flourish. Patience: Patience at BTS embodies a multifaceted approach that encompasses trust, readiness to play a role effectively, striving to reach one's potential, a hunger for success, and a helpful disposition. It encourages individuals to cultivate a patient attitude, fostering a work environment where goals are pursued with persistence and determination. Genuine Excitement: Genuine excitement at BTS manifests as a contagious enthusiasm that permeates the organization. It is characterized by a deep-seated passion for one's work, fostering a positive and vibrant work environment where individuals are energized and motivated to make a meaningful impact through their roles. Being Helpful: Being helpful at BTS entails proactively identifying opportunities to assist, be it in aiding clients with their concerns or supporting team members in their roles. It fosters a collaborative and supportive work environment, where individuals are attuned to the needs of others and are ready to step in to provide assistance.

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