Locations of Objects in Showcase

What is a Hurricane, Typhoon, or Tropical Cyclone? The terms "hurricane" and "typhoon" are regionally specific names for a strong "tropical cyclone". A tropical cyclone is the generic term for a non-frontal synoptic scale low-pressure system over tropical or sub-tropical waters with organized convection (i.e. thunderstorm activity) and definite cyclonic surface wind circulation (Holland 1993). Tropical cyclones with maximum sustained surface winds of less than 17 m/s (34 kt, 39 mph) are usually called "tropical depressions" (This is not to be confused with the condition mid-latitude people get during a long, cold and grey winter wishing they could be closer to the equator). Once the tropical cyclone reaches winds of at least 17 m/s (34 kt, 39 mph) they are typically called a "tropical storm" or in Australia a Category 1 cyclone and are assigned a name. If winds reach 33 m/s (64 kt, 74 mph), then they are called: "hurricane" (the North Atlantic Ocean, the Northeast Pacific Ocean east of the dateline, or the South Pacific Ocean east of 160E) "typhoon" (the Northwest Pacific Ocean west of the dateline) "severe tropical cyclone" or "Category 3 cyclone" and above (the Southwest Pacific Ocean west of 160°E or Southeast Indian Ocean east of 90°E) "very severe cyclonic storm" (the North Indian Ocean) "tropical cyclone" (the Southwest Indian Ocean) Coriolis Effect The Coriolis Effect—the deflection of an object moving on or near the surface caused by the planet’s spin—is important to fields, such as meteorology and oceanography. Storm Approaching Southeast Asia Because of the Coriolis Effect, hurricanes spin counterclockwise in the Northern Hemisphere, while these types of storms spin clockwise in the Southern Hemisphere. This Northern Hemisphere storm, approaching Southeast Asia, is spinning counterclockwise. Earth is a spinning planet, and its rotation affects climate, weather, and the ocean through the Coriolis Effect. Named after the French mathematician Gaspard Gustave de Coriolis (born in 1792), the Coriolis Effect refers to the curved path that objects moving on Earth’s surface appear to follow because of the spinning of the planet. As Earth turns, points near the equator—countries like Ecuador and Kenya—are moving much faster than places near the planet’s poles. This is because Earth is shaped like a marble: Its circumference is larger near its middle (the equator) than near its top and bottom. All places on Earth experience a day that is about 24 hours long, but points near the equator have to travel longer distances in the same period of time, which means that those places move faster. Scientists say these points have more “angular momentum.” This is why rockets are usually launched from places near the equator, like Cape Canaveral, Florida, United States. Such locations give rockets a large initial speed, which helps them get into orbit using the least possible amount of fuel. The Coriolis Effect influences wind patterns, which in turn dictate how ocean currents move. Imagine wind near the equator flowing to the north. That wind starts with a certain speed due to Earth’s rotation (near the equator, Earth rotates at a speed of roughly 1,600 kilometers per hour (1,000 miles per hour) from west to east). As the wind travels north toward the North Pole, it moves over parts of Earth that are rotating progressively more slowly. Since the wind retains its angular momentum, it keeps moving from west to east, overtaking the part of Earth turning more slowly below it. As a result, the wind appears to bend to the east (that is, to the right). This is the Coriolis Effect in action. Wind flowing south from the equator would likewise bend to the east. This effect is responsible for many meteorological and oceanographic phenomena. For instance, due to the Coriolis Effect, hurricanes in the Northern Hemisphere spin in a counterclockwise direction, while hurricanes in the Southern Hemisphere (known as cyclones) spin in a clockwise direction. Ocean-circling currents known as “gyres” also spin in spiral patterns thanks to the Coriolis Effect. There is an urban legend that water in toilets spins in opposite directions in the Northern and Southern Hemispheres because of the Coriolis Effect. But that isn't true—a toilet bowl is too small for the effect to be observed. Instead, other factors like the shape of the toilet bowl and the direction that the water enters are largely responsible for how the flushing water moves.

What is an earthquake? Would you be surprised to learn that several million earthquakes happen every year? Seriously. Most are so small in magnitude or size that we cannot even feel them. In fact, only 20 earthquakes are efficiently reported each year in the United States Geological Survey. Wow! That is a huge difference! The Earth has four major layers. Inner core, outer core, mantle, and crust. Think of the crust and top of the mantle like the skin of the earth. This skin is made up of different pieces of rock called tectonic plates. There are about 15 major slabs that join together, kind of like a puzzle. The edges around the tectonic plates are called plate boundaries. These massive pieces of rock slide back and forth under the Earth's surface, bumping up against each other and creating a lot of tension. This tension and movement create faults, which are basically huge cracks in the rock. When the faults get stuck, they build up pressure. And when they get unstuck, you guessed it, an earthquake. So basically, an earthquake is caused by the shifting and sliding of tectonic plates on the Earth's upper mantle and crust. There are three ways that tectonic plates shift or slide. They are subduction, lateral sliding, and spreading. Subduction happens when plates crash into each other. This can cause one plate to slide under another and be destroyed. Or the edges of the plate may rise up and form mountains. Lateral sliding means that the plates slide alongside each other, which can create lots of friction. And like you might have guessed, spreading happens when plates move apart from each other. When they do, melted rock between the plates rises and cools, forming new crust. Here's an interesting fact. Nearly 90% of all earthquakes begin in the Pacific Ocean, in an area called the Ring of Fire. It's called the Ring of Fire because along with earthquakes, it's filled with many active volcanoes. More than 450! Earthquakes can be powerful enough to change the surface of the earth and can do a lot of damage. And sometimes earthquakes can even cause other natural disasters, like avalanches, landslides, and tsunamis. Pretty wild, right? The epicenter is the location of an earthquake on the Earth's surface. The closer you are to the epicenter, the more of the earthquake you will feel. Earthquakes lose intensity as they travel away from the epicenter. Scientists measure the intensity of an earthquake using a special device called a seismograph. Seismometers detect and measure the vibrations given off by an earthquake. Magnitude is the number given to record the size of an earthquake. For example, a magnitude 5.5 is considered moderate. Above 8.0 is considered a major earthquake and we see one every year or two. Earthquakes measured at 2.5 or less are usually not felt, but can be recorded. And believe it or not, there are millions that happen each year. You can make a model of a seismograph at home, and we are going to show you how. It's activity time! You can print off directions for this one on our website at learnbright.org. You'll need a cardboard box, string, a plastic cup, a marker, small heavy objects, a long strip of paper, and a friend because this is an activity for at least two people. Now comes the fun part. One friend shakes the box, alternating between hard and soft and slow and fast, while the other friend is pulling the strip of paper through the bottom. Watch the marker as it records the movement. This is exactly what a seismograph does during an earthquake. So, in a way, we have not only created our own seismograph, but our own earthquake as well. Now, we can analyze the data just like scientists. Can you tell how hard the box was shaking based on the line? Can you tell when it was barely shaking at all? You are on your way to becoming a seismologist. A seismologist is a person that studies earthquakes. It's pretty cool to watch the process, but it's even more exciting to do it yourself. You can head on over to our website to get detailed instructions for this activity. Just download the lesson plan and as always have fun! Hope you had fun learning with us! Visit us at learnbright.org for thousands of Hope you had fun learning with us! Visit us at learnbright.org for thousands of free resources and turnkey solutions for teachers and homeschoolers.

To the Lakota, and other indigenous people on North America's Great Plains, the bison was an essential part of their culture ( expressed in the quote on the previous page). The bison provided meat for nutrition, a hide for clothing and shelter, bones for tools, and fat for soap. The bison was also central to their religious beliefs. So, when European settlers hunted the bison nearly to extinction, Lakota culture suffered. Culture is central to a society and the identity of its people, as well as its continued existence. Therefore, geographers study culture as a way to understand similarities and differences among societies across the world, and in some cases, to help preserve these societies. Analyzing Culture All of a group's learned behaviors, actions, beliefs, and objects are a part of culture. It is a visible force seen in a group's actions, possessions, and influence on the landscape. For example, in a large city you can see people working in offices, factories, and stores, and living in high-rise apartments or suburban homes. You might observe them attending movies, concerts, or sporting events. Culture is also an invisible force guiding people through shared belief systems, customs, and traditions. Culture is learned, in that it develops through experiences, and not merely transmitted through genetics. For example, many people in the United States have developed a strong sense of competitiveness in school and business, and believe that hard work is a key to success. These types of elements, visible and invisible, are cultural traits. A series of interrelated traits make up a cultural complex, such as the process of steps and acceptable behaviors related to greeting a person in different cultures. A single cultural artifact, such as an automobile, may represent many different values, beliefs, behaviors and traditions and be representative of a cultural complex. Since culture is learned there are many ways that one generation passes its culture to the next. Children and adults learn traits three ways: • imitation, as when learning a language by repeating sounds or behaviors from a person or television • informal instruction, as when a parent reminds a child to say "please" • formal instruction, as when students learn history in school 132 HUMAN GEOGRAPHY: AP" EDITION CULTURAL COMPLEX OF THE AUTOMOBILE The automobile provides much more than just transportation, as it reflects many values that are central to American culture. Origins of Culture The area in which a unique culture or a specific trait develops is a culture hearth. Classical Greece was a culture hearth for democracy more than 2,000 years ago. New York City was a culture hearth for rap music in the 1970s. Geographers study how cultures develop in hearths and diffuse-or spread-to other places. Geographers also study taboos, behaviors heavily discouraged by a culture. For example, many cultures have taboos against eating certain foods, such as pork or insects. What is considered taboo changes over time. In the United States, marriages between Protestants and Catholics were once taboo, but they are not widely opposed now. Traditional, Folk, and Indigenous Cultures With the beginning of the Industrial Revolution in the late 18th century, modern transportation and communication connected people as never before and led to extensive cultural mixing, especially as cities have grown. The world prior to this time was very different; however, remnants of the past are still evident in our modern cultures. Traditional, folk, and indigenous cultures share some important characteristics and are often grouped together, but they do have some subtle differences. Traditional Culture Recently, the meanings of traditional, folk, and indigenous culture have begun to merge, causing geographers to debate when each should be used. Increasingly, the term traditional culture is used to encompass all three cultural designations. All three types share the function of passing down long-held beliefs, values, and practices and are generally resistant to rapid changes in their culture. Folk Culture The beliefs and practices of small, homogenous groups of people, often living in rural areas that are relatively isolated and slow to change, are known as folk cultures. Like all cultures, they demonstrate the diverse ways that people have adapted to a physical environment. For example, people around the world learned to make shelters out of available resources, whether 3.1: INTRODUCTION TO CULTURE 133 it was snow or mud bricks or wood. However, people used similar resources such as wood differently. In Scandinavia, people used trees to build cabins. In the American Midwest, people processed trees into boards, built a frame, and attached the boards to it. Many traits of folk culture continue today. Corn was first grown in Mexico around 10,000 years ago, and it is still grown there today. While many elements of folk culture exist side by side with modern culture, there are people whose societies have changed little, if at all, from long ago. These people practice traditional cultures, those which have not been affected by modern technology or influences. They often live in remote regions, such as some small tribes in the Amazon rainforest, and have scant knowledge of the outside world. As the lines continue blurring between cultural designations, the Amish of Pennsylvania are often referenced as both folk and traditional culture. Indigenous Culture When members of an ethnic group reside in their ancestral lands, and typically possess unique cultural traits, such as speaking their own exclusive language, they are considered an indigenous culture. Some indigenous peoples have been displaced from their native lands, but still practice their indigenous culture. Native Americans in the United States, such as the Navajo, have kept indigenous cultural practices. First Nations of Canada, such as the Inuit, have also retained their indigenous culture. Globalization and Popular Culture As a result of the Industrial Revolution, improvements in transportation and communication have shortened the time required for movement, trade, or other forms of interaction between two places. This development, known as space-time compression (see Topics 1.4 and 3.6), has accelerated culture change around the world. In 1817, a freight shipment from Cincinnati needed 52 days to reach New York City. By 1850, because of canals and railroads, it took half that long. And by 1852, it took only 7 days. Today, an airplane flight takes only a few hours, and digital information takes seconds or less. Similar change has occurred on the global scale. People travel freely across the world in a matter of hours, and communication has advanced to a point where people share information instantaneously across the globe. The increased global interaction has had a profound impact on cultures, from spreading English across the world to instant sharing of news, events and music. Globalization specifically refers to the increased integration of the world economy since the 1970s. The process of intensified interaction among peoples, governments, and companies of different countries around the globe has had profound impacts on culture. The culture of the United States is intertwined with globalization. Through the influence of its corporations, Hollywood movies, and government, the United States exerts widespread influence in other countries. But other countries also shape American culture. For example, in 2019, the National Basketball Association included players from 38 countries or territories. When cultural traits- such as clothing, music, movies, and types of 134 HUMAN GEOGRAPHY: AP. EDITION businesses-spread quickly over a large area and are adopted by various groups, they become part of popular culture. Elements of popular culture often begin in urban areas and diffuse quickly through globalization processes such as the media and Internet. These elements can quickly be adopted worldwide, making them part of global culture. People around the world follow European soccer, Indian Bollywood movies, and Japanese animation known as anime. With people in many nations wearing similar clothes, listening to similar music, and eating similar food, popular cultural traits often promote uniformity in beliefs, values, and the cultural landscape across many places The cultural landscape, also known as the built environment (see Topic 3.2), is the modification of the environment by a group and is a visible reflection of that group's cultural beliefs and values. Traditional Culture to Popular Culture Popular culture emphasizes trying what is new rather than preserving what is traditional. Many people, especially older generations or those who follow a folk culture, openly resist the adoption of popular cultural traits. They do this by preserving traditional languages, religions, values, and foods. While older generations often resist the adoption of popular culture, they seldom are successful in keeping their traditional cultures from changing, especially among the young people of their society. One clash between popular and traditional culture is occurring in Brazil. As the population expands to the interior of the rain forest, many indigenous cultures, like the Yanamamo tribe, have more contact with outside groups. Remaining isolated by the forest is becoming increasingly difficult as many young people from the indigenous cultures become exposed to popular culture and begin to integrate into the larger Brazilian society. As the young people leave their communities, they are more likely to accept popular culture at the expense of their indigenous cultural heritage, which threatens the very existence of their folk culture. Traditional culture typically exhibits horizontal diversity, meaning each traditional culture has its own customs and language that makes it distinct from other culture groups. Yet, people people within each group are usually homogeneous, or very similar to each other. By contrast, popular culture typically exhibits vertical diversity, meaning that modern urban societies are usually heterogeneous, or exhibiting differences, within the society and usually contain numerous multiethnic neighborhoods. However, on a global scale popular cultures are relatively similar with the same type of malls, shops, fast food, and clothing. Urban global culture centers are not identical, yet, global cities often do not have as much horizontal diversity across space as folk cultures. 3.1: INTRODUCTION TO CULTURE 135 COMPARING TRADITIONAL AND POPULAR CULTURE Trait Traditional Culture Popular or Global Culture Society • Rural and isolated location • Urban and connected location • Homogeneous and • Diverse and multiethnic indigenous population population • Most people speak an • Many people speak a global indigenous or ethnic local language such as English or language Arabic • Horizontal diversity • Vertical diversity Social • Emphasis on community and • Emphasis on individualism and Structure conformity making choices • Families live close to each • Dispersed families other • Weakly defined gender roles • Well-defined gender roles Diffusion • Relatively slow and limited • Relatively rapid and extensive • Primarily through relocation • Often hierarchical • Oral traditions and stories • Social media and mass media Buildings and • Materials produced locally, • Materials produced in distant Housing such as stone or grass factories, such as steel or glass • Built by community or owner • Built by a business • Similar style for community • Variety of architectural styles • Different between cultures • Similar between cities • Traditional architecture • Postmodern / contemporary architecture Food • Locally produced • Often imported • Choices limited by tradition • Wide range of choice • Prepared by the family or • Purchased in restaurants community Spatial Focus • Local and regional • National and global Artifacts, Mentifacts, and Sociofacts Whether a cultural attribute is considered traditional, folk, indigenous, or popular in nature, it is valuable to differentiate between elements of culture that can be seen and those that can not. There are artifacts that comprise the material culture, which consists of tangible things, or those that can be experienced by the senses. Art, clothing, food, music, sports, and housing types are all tangible elements of culture. Another element of the study of artifacts is understanding the techniques to use or build a specific artifact. Artifacts can be unique to a particular culture, or can be shared. For example, people of all cultures need to communicate through language, yet there are many groups that possess languages unique to their culture. The ability to read, write and understand the English language is an artifact of importance for much of popular global culture. 136 HUMAN GEOGRAPHY: AP" EDITION Mentifacts comprise a group's nonmaterial culture and consist ofintangible concepts, or those not having a physical presence. Beliefs, values, practices, and aesthetics (pleasing in appearance) determine what a cultural group views as acceptable and desirable. Mentifacts can also be unique or shared. People of many cultures possess an belief in one or many deities, and often the deities are unique to that culture. The belief in a god is a mentifact-the religious building or symbols are artifacts. Cultural groups also possess sociofacts, which are the ways people organize their society and relate to one another. Taken altogether, people tend to see the whole of their culture as greater than the sum of its individual parts. Sociofacts are embodied through families, governments, sports teams, religious organizations, education systems, and other social constructs. As with artifacts and mentifacts, sociofacts may also be unique or similar to other societies. Families are the foundations of most societies, yet what constitutes the structure of a family may vary widely between cultural groups. For example, Western cultures tend to view the nuclear family, consisting of the parents and their children as the basic family unit. By contrast, in many Western African cultures the norm is the extended family, consisting of several generations and other family members such as cousins living under one roof.

Important Preparations Before an Earthquake Strikes • Follow the structural design and engineering practices when constructing a house or building. • Evaluate the structural soundness of the buildings and houses: strengthen if necessary. • Be aware of the earthquake evacuation plans for all of the buildings you occupy regularly. • Strap or bolt heavy furniture and cabinets to the wall to keep them in place. • Breakable items, harmful chemical, and flammable materials should be stored properly in the lowermost secure shelves • Prepare and know where fire extinguishers, first aid kits, alarms, and communication facilities are located and learn how to use them beforehand. • Pick safe places in each room of your home, workplace, and school and practice doing drop, cover, and hold.Essential Things to Do While an Earthquake is Happening • Stay calm. • Duck under a sturdy desk or table and hold onto it. Protect your head with your arms. • If there is no sturdy furniture, sit on the floor in a corner next to an interior wall and cover your head and neck with your arms. • Move away from glass windows, sliding doors, shelves, cabinets, and other heavy objects. • Grab anything handy to shield your head and face from falling debris and splinting glass. • Stay indoors until the shaking stops. If you must leave the building. use the stairs rather than elevators. • Stay away from trees, power lines, posts, and concrete structures and proceed cautiously to an open area. • Move away from steep. slopes, which may be affected by landslides. • Move quickly to higher grounds since tsunamis might follow • Pull over to a clear location and stop. Avoid bridges, overpasses, and power lines, if possible. • Be updated about disaster. prevention instructions from battery operated radios.Essential Safety Measures After an Earthquake • Check yourself and others for injuries. • Do not panic. • Expect and prepare for aftershocks. These aftershocks may be weaker but they may sometimes cause more damage than the major earthquake. • Look for emergency supply kits. They should include food, water, medication, clothing, and other things you may need. • If you need to evacuate, leave a message stating where you are going • Do not enter damaged buildings since they might have weakened foundations, increasing their susceptibility for collapse. There can also be a lot of falling debris. • Do not use elevators • Check water and electrical lines for damages. Turn the main switch off to avoid any incidences of electric shock • Look for and extinguish fires to reduce their chances of spreading. • Avoid fallen power lines. • Tune in to radio broadcasts and be updated on disaster prevention instructions.

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

Properties and Locations of Solar System Objects

Location of Objects

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