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    MCAT General Chemistry Review 2025-2026: Online + Book
    MCAT General Chemistry Review 2025-2026: Online + Book
    MCAT General Chemistry Review 2025-2026: Online + Book
    Ebook1,090 pages11 hours

    MCAT General Chemistry Review 2025-2026: Online + Book

    By Kaplan Test Prep

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    About this ebook

    Kaplan’s MCAT General Chemistry Review 2024-2025 offers an expert study plan, detailed subject review, and hundreds of online and in-book practice questions—all authored by the experts behind Kaplan's score-raising MCAT prep course.

    Prepping for the MCAT is a true challenge. Kaplan can be your partner along the way—offering guidance on where to focus your efforts and how to organize your review. This book has been updated to match the AAMC’s guidelines precisely—no more worrying about whether your MCAT review is comprehensive!

    The Most Practice
    • More than 350 questions in the book and access to even more online—more practice than any other MCAT general chemistry book on the market.

    The Best Practice
    • Comprehensive general chemistry subject review is written by top-rated, award-winning Kaplan instructors.
    • Full-color, 3-D illustrations, charts, graphs and diagrams help turn even the most complex science into easy-to-visualize concepts.
    • All material is vetted by editors with advanced science degrees and by a medical doctor.
    • Online resources, including a full-length practice test, help you practice in the same computer-based format you’ll see on Test Day.

    Expert Guidance
    • High-yield badges throughout the book identify the topics most frequently tested by the AAMC.
    • We know the test: The Kaplan MCAT team has spent years studying every MCAT-related document available. 
    • Kaplan’s expert psychometricians ensure our practice questions and study materials are true to the test.
       
    LanguageEnglish
    PublisherKaplan Test Prep
    Release dateJul 2, 2024
    ISBN9781506294216
    MCAT General Chemistry Review 2025-2026: Online + Book

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      Book preview

      MCAT General Chemistry Review 2025-2026 - Kaplan Test Prep

      SCIENCE MASTERY ASSESSMENT

      Every pre-med knows this feeling: there is so much content I have to know for the MCAT! How do I know what to do first or what's important?

      While the high-yield badges throughout this book will help you identify the most important topics, this Science Mastery Assessment is another tool in your MCAT prep arsenal. This quiz (which can also be taken in your online resources) and the guidance below will help ensure that you are spending the appropriate amount of time on this chapter based on your personal strengths and weaknesses. Don't worry though— skipping something now does not mean you'll never study it. Later on in your prep, as you complete full-length tests, you'll uncover specific pieces of content that you need to review and can come back to these chapters as appropriate. 

      How to Use This Assessment

      If you answer 0–7 questions correctly:

      Spend about 1 hour to read this chapter in full and take limited notes throughout. Follow up by reviewing all quiz questions to ensure that you now understand how to solve each one.

      If you answer 8–11 questions correctly:

      Spend 20–40 minutes reviewing the quiz questions. Beginning with the questions you missed, read and take notes on the corresponding subchapters. For questions you answered correctly, ensure your thinking matches that of the explanation and you understand why each choice was correct or incorrect.

      If you answer 12–15 questions correctly:

      Spend less than 20 minutes reviewing all questions from the quiz. If you missed any, then include a quick read-through of the corresponding subchapters, or even just the relevant content within a subchapter, as part of your question review. For questions you answered correctly, ensure your thinking matches that of the explanation and review the Concept Summary at the end of the chapter.

      Which of the following is the correct electron configuration for Zn²+?

      1s²2s²2p⁶3s²3p⁶4s⁰3d¹⁰

      1s²2s²2p⁶3s²3p⁶4s²3d⁸

      1s²2s²2p⁶3s²3p⁶4s²3d¹⁰

      1s²2s²2p⁶3s²3p⁶4s⁰3d⁸

      Which of the following quantum number sets is possible?

      n = 2; l = 2; ml = 1; ms=+12

      n = 2; l = 1; ml = −1; ms=+12

      n = 2; l = 0; ml = −1; ms=−12

      n = 2; l = 0; ml = 1; ms=−12

      What is the maximum number of electrons allowed in a single atomic energy level in terms of the principal quantum number n ?

      2n

      2n + 2

      2n²

      2n² + 2

      Which of the following equations describes the maximum number of electrons that can fill a subshell?

      2l + 2

      4l + 2

      2l²

      2l² + 2

      Which of the following atoms only has paired electrons in its ground state?

      Sodium

      Iron

      Cobalt

      Helium

      An electron returns from an excited state to its ground state, emitting a photon at λ = 500 nm. What would be the magnitude of the energy change if one mole of these photons were emitted? (Note: h = 6.626 × 10−34 J · s, NA = 6.02 × 10²³ mol−1)

      3.98 × 10−21 J

      3.98 × 10−19 J

      2.39 × 10³ J

      2.39 × 10⁵ J

      Suppose an electron falls from n = 4 to its ground state, n = 1. Which of the following effects is most likely?

      A photon is absorbed.

      A photon is emitted.

      The electron moves into a p-orbital.

      The electron moves into a d-orbital.

      Which of the following isotopes of carbon is LEAST likely to be found in nature?

      ⁶C

      ¹²C

      ¹³C

      ¹⁴C

      Which of the following best explains the inability to measure position and momentum exactly and simultaneously according to the Heisenberg uncertainty principle?

      Imprecision in the definition of the meter and kilogram

      Limits on accuracy of existing scientific instruments

      Error in one variable is increased by attempts to measure the other

      Discrepancies between the masses of nuclei and of their component particles

      Which of the following electronic transitions would result in the greatest gain in energy for a single hydrogen electron?

      An electron moves from n = 6 to n = 2.

      An electron moves from n = 2 to n = 6.

      An electron moves from n = 3 to n = 4.

      An electron moves from n = 4 to n = 3.

      Suppose that an atom fills its orbitals as shown:

      3s orbital has two electrons; 3p has three orbitals, each of which has one electron

      Such an electron configuration most clearly illustrates which of the following laws of atomic physics?

      Hund’s rule

      Heisenberg uncertainty principle

      Bohr model

      Rutherford model

      How many total electrons are in a ¹³³Cs cation?

      54

      55

      78

      132

      The atomic weight of hydrogen is 1.008 amu. What is the percent composition of hydrogen by isotope, assuming that hydrogen’s only isotopes are ¹H and ²D?

      92% H, 8% D

      99.2% H, 0.8% D

      99.92% H, 0.08% D

      99.992% H, 0.008% D

      Consider the two sets of quantum numbers shown in the table, which describe two different electrons in the same atom.

      Which of the following terms best describes these two electrons?

      Parallel

      Opposite

      Antiparallel

      Paired

      Which of the following species is represented by the electron configuration 1s²2s²2p⁶3s²3p⁶4s¹3d⁵?

      Cr

      Mn+

      Fe²+

      I only

      I and II only

      II and III only

      I, II, and III

      Answer Key

      A

      B

      C

      B

      D

      D

      B

      A

      C

      B

      A

      A

      B

      A

      B

      CHAPTER 1

      ATOMIC STRUCTURE

      In This Chapter

      1.1 Subatomic Particles

      Protons

      Neutrons

      Electrons

      1.2 Atomic Mass vs. Atomic Weight

      Atomic Mass

      Atomic Weight

      1.3 Rutherford, Planck, and Bohr

      Bohr Model

      Applications of the Bohr Model

      1.4 Quantum Mechanical Model of Atoms

      Quantum Numbers

      Electron Configurations

      Hund’s Rule

      Valence Electrons

      Concept Summary

      CHAPTER PROFILE

      Pie chart indicating the content in this chapter should be relevant to about six percent of all questions about General Chemistry on the MCAT

      The content in this chapter should be relevant to about 7% of all questions about general chemistry on the MCAT.

      This chapter covers material from the following AAMC content category:

      4E: Atoms, nuclear decay, electronic structure, and atomic chemical behavior

      Introduction

      Chemistry is the investigation of the atoms and molecules that make up our bodies, our possessions, the food we eat, and the world around us. There are different branches of chemistry, three of which are tested directly on the MCAT: general (inorganic) chemistry, organic chemistry, and biochemistry. Ultimately, all investigations in chemistry are seeking to answer the questions that confront us in the form—the shape, structure, mode, and essence—of the physical world that surrounds us.

      Many students feel similarly about general chemistry and physics: But I’m premed, they say. Why do I need to know any of this? What good will this be when I’m a doctor? Do I only need to know this for the MCAT? Recognize that to be an effective doctor, one must understand the physical building blocks that make up the human body. Pharmacologic treatment is based on chemistry; many diagnostic tests used every day detect changes in the chemistry of the body.

      So, let’s get down to the business of learning and remembering the principles of the physical world that help us understand what all this stuff is, how it works, and why it behaves the way it does—at both the molecular and macroscopic levels. In the process of reading through these chapters and applying your knowledge to practice questions, you’ll prepare yourself for success not only on the Chemical and Physical Foundations of Biological Systems section of the MCAT but also in your future career as a physician.

      This first chapter starts our review of general chemistry with a consideration of the fundamental unit of matter—the atom. First, we focus on the subatomic particles that make it up: protons, neutrons, and electrons. We will also review the Bohr and quantum mechanical models of the atom, with a particular focus on the similarities and differences between them.

      MCAT EXPERTISE

      The building blocks of the atom are also the building blocks of knowledge for the general chemistry concepts tested on the MCAT. By understanding these particles, we will be able to use that knowledge as the nucleus of understanding for all of general chemistry.

      1.1 Subatomic Particles

      LEARNING OBJECTIVES

      After Chapter 1.1, you will be able to:

      Identify the subatomic particles most important for determining various traits of an atom, including charge, atomic number, and isotope

      Determine the number of protons, neutrons, and electrons within an isotope, such as ¹⁴C

      Although you may have encountered in your university-level chemistry classes such subatomic particles as quarks, leptons, and gluons, the MCAT’s approach to atomic structure is much simpler. There are three subatomic particles that you must understand: protons, neutrons, and electrons.

      substance made of atoms, which have a nucleus in the center

      Figure 1.1. Matter: From Macroscopic to Microscopic

      Protons

      Protons are found in the nucleus of an atom, as shown in Figure 1.1. Each proton has an amount of charge equal to the fundamental unit of charge (e = 1.6 × 10−19 C), and we denote this fundamental unit of charge as "+1 e or simply +1" for the proton. Protons have a mass of approximately one atomic mass unit (amu). The atomic number (Z) of an element, as shown in Figure 1.2, is equal to the number of protons found in an atom of that element. As such, it acts as a unique identifier for each element because elements are defined by the number of protons they contain. For example, all atoms of oxygen contain eight protons; all atoms of gadolinium contain 64 protons. While all atoms of a given element have the same atomic number, they do not necessarily have the same mass—as we will see in our discussion of isotopes.

      K with 19 above it and 39.1 below it

      Figure 1.2. Potassium, from the Periodic Table

      Potassium has the symbol K (Latin: kalium), atomic number 19, and atomic weight of approximately 39.1.

      Neutrons

      Neutrons, as the name implies, are neutral—they have no charge. A neutron’s mass is only slightly larger than that of the proton, and together, the protons and the neutrons of the nucleus make up almost the entire mass of an atom. Every atom has a characteristic mass number (A), which is the sum of the protons and neutrons in the atom’s nucleus. A given element can have a variable number of neutrons; thus, while atoms of the same element always have the same atomic number, they do not necessarily have the same mass number. Atoms that share an atomic number but have different mass numbers are known as isotopes of the element, as shown in Figure 1.3. For example, carbon (Z = 6) has three naturally occurring isotopes: 6 12 C , with six protons and six neutrons; 6 13 C , with six protons and seven neutrons; and 6 14 C , with six protons and eight neutrons. The convention Z A X is used to show both the atomic number (Z) and the mass number (A) of atom X.

      protium (H-1), deuterium (H-2), tritium (H-3)

      Figure 1.3. Various Isotopes of Hydrogen

      Atoms of the same element have the same atomic number (Z = 1) but may have varying mass numbers (A = 1, 2, or 3).

      Electrons

      Electrons move through the space surrounding the nucleus and are associated with varying levels of energy. Each electron has a charge equal in magnitude to that of a proton, but with the opposite (negative) sign, denoted by "−1 e or simply –1." The mass of an electron is approximately 1 2000 that of a proton. Because subatomic particles’ masses are so small, the electrostatic force of attraction between the unlike charges of the proton and electron is far greater than the gravitational force of attraction based on their respective masses.

      Electrons move around the nucleus at varying distances, which correspond to varying levels of electrical potential energy. The electrons closer to the nucleus are at lower energy levels, while those that are further out (in higher electron shells) have higher energy. The electrons that are farthest from the nucleus have the strongest interactions with the surrounding environment and the weakest interactions with the nucleus. These electrons are called valence electrons; they are much more likely to become involved in bonds with other atoms because they experience the least electrostatic pull from their own nucleus. Generally speaking, the valence electrons determine the reactivity of an atom. As we will discuss in Chapter 3 of MCAT General Chemistry Review, the sharing or transferring of these valence electrons in bonds allows elements to fill their highest energy level to increase stability. In the neutral state, there are equal numbers of protons and electrons; losing electrons results in the atom gaining a positive charge, while gaining electrons results in the atom gaining a negative charge. A positively charged atom is called a cation, and a negatively charged atom is called an anion.

      BRIDGE

      Valence electrons will be very important to us in both general and organic chemistry. Knowing how tightly held those electrons are will allow us to understand many of an atom’s properties and how it interacts with other atoms, especially in bonding. Bonding is so important that it is discussed in Chapter 3 of both MCAT General Chemistry Review and MCAT Organic Chemistry Review.

      Some basic features of the three subatomic particles are shown in Table 1.1.

      Table 1.1. Subatomic Particles

      Example: Determine the number of protons, neutrons, and electrons in a nickel-58 atom and in a nickel-60 +2 cation.

      Solution: ⁵⁸Ni has an atomic number of 28 and a mass number of 58. Therefore, ⁵⁸Ni will have 28 protons, 28 electrons, and 58 – 28, or 30, neutrons.

      ⁶⁰Ni²+ has the same number of protons as the neutral ⁵⁸Ni atom. However, ⁶⁰Ni²+ has a positive charge because it has lost two electrons; thus, Ni²+ will have 26 electrons. Also, the mass number is two units higher than for the ⁵⁸Ni atom, and this difference in mass must be due to two extra neutrons; thus, it has a total of 32 neutrons.

      BRIDGE

      Solutions to concept checks for a given chapter in MCAT General Chemistry Review can be found near the end of the chapter in which the concept check is located, following the Concept Summary for that chapter.

      MCAT CONCEPT CHECK 1.1:

      Before you move on, assess your understanding of the material with these questions.

      Which subatomic particle is the most important for determining each of the following properties of an atom?

      Charge: ________________________________

      Atomic number: ________________________________

      Isotope: ____________________________

      In nuclear medicine, isotopes are created and used for various purposes; for instance, ¹⁸O is created from ¹⁸F. Determine the number of protons, neutrons, and electrons in each of these species.

      1.2 Atomic Mass vs. Atomic Weight

      LEARNING OBJECTIVES

      After Chapter 1.2, you will be able to:

      Describe atomic mass and atomic weight

      Recall the units of molar mass

      Predict the number of protons, neutrons, and electrons in a given isotope

      There are a few different terms used by chemists to describe the heaviness of an element: atomic mass and mass number, which are essentially synonymous, and atomic weight. While the atomic weight is a constant for a given element and is reported in the periodic table, the atomic mass or mass number varies from one isotope to another. In this section, carefully compare and contrast the different definitions of these terms—because they are similar, they can be easy to mix up on the MCAT.

      KEY CONCEPT

      Atomic number (Z) = number of protons

      Mass number (A) = number of protons + number of neutrons

      Number of protons = number of electrons (in a neutral atom)

      Electrons are not included in mass calculations because they are much smaller.

      Atomic Mass

      As we’ve seen, the mass of one proton is approximately one amu. The size of the atomic mass unit is defined as exactly 1 12 the mass of the carbon-12 atom, approximately 1.66 × 10−24 g. Because the carbon-12 nucleus has six protons and six neutrons, an amu is approximately equal to the mass of a proton or a neutron. The difference in mass between protons and neutrons is extremely small; in fact, it is approximately equal to the mass of an electron.

      The atomic mass of an atom (in amu) is nearly equal to its mass number, the sum of protons and neutrons (in reality, some mass is lost as binding energy, as discussed in Chapter 9 of MCAT Physics and Math Review). Atoms of the same element with varying mass numbers are called isotopes (from the Greek for same place). Isotopes differ in their number of neutrons and are referred to by the name of the element followed by the mass number; for example, carbon-12 or iodine-131. Only the three isotopes of hydrogen, shown in Figure 1.3, are given unique names: protium (Greek: first) has one proton and an atomic mass of 1 amu; deuterium (second) has one proton and one neutron and an atomic mass of 2 amu; tritium (third) has one proton and two neutrons and an atomic mass of 3 amu. Because isotopes have the same number of protons and electrons, they generally exhibit similar chemical properties.

      Atomic Weight

      In nature, almost all elements exist as two or more isotopes, and these isotopes are usually present in the same proportions in any sample of a naturally occurring element. The weighted average of these different isotopes is referred to as the atomic weight and is the number reported on the periodic table. For example, chlorine has two main naturally occurring isotopes: chlorine-35 and chlorine-37. Chlorine-35 is about three times more abundant than chlorine-37; therefore, the atomic weight of chlorine is closer to 35 than 37. On the periodic table, it is listed as 35.5. Figure 1.4 illustrates the half-lives of the different isotopes of the elements; because half-life corresponds with stability, it also helps determine the relative proportions of these different isotopes.

      plot of neutrons vs. protons; slope is steeper than a line of neutrons = protons

      Figure 1.4. Half-Lives of the Different Isotopes of Elements

      Half-life is a marker of stability; generally, longer-lasting isotopes are more abundant.

      KEY CONCEPT

      When an element has two or more isotopes, no one isotope will have a mass exactly equal to the element’s atomic weight. Bromine, for example, is listed in the periodic table as having a mass of 79.9 amu. This is an average of the two naturally occurring isotopes, bromine-79 and bromine-81, which occur in almost equal proportions. There are no bromine atoms with an actual mass of 79.9 amu.

      The utility of the atomic weight is that it represents both the mass of the average atom of that element, in amu, and the mass of one mole of the element, in grams. A mole is a number of things (atoms, ions, molecules) equal to Avogadro’s number, NA = 6.02 × 10²³. For example, the atomic weight of carbon is 12.0 amu, which means that the average carbon atom has a mass of 12.0 amu (carbon-12 is far more abundant than carbon-13 or carbon-14), and 6.02 × 10²³ carbon atoms have a combined mass of 12.0 grams.

      MNEMONIC

      Atomic mass is nearly synonymous with mass number. Atomic weight is a weighted average of naturally occurring isotopes of that element.

      Example: Element Q consists of three different isotopes: A, B, and C. Isotope A has an atomic mass of 40 amu and accounts for 60 percent of naturally occurring Q. Isotope B has an atomic mass of 44 amu and accounts for 25 percent of Q. Finally, isotope C has an atomic mass of 41 amu and accounts for 15 percent of Q. What is the atomic weight of element Q?

      Solution: The atomic weight is the weighted average of the naturally occurring isotopes of that element:

      0.60 (40 amu) + 0.25 (44 amu) + 0.15 (41 amu) = 24.00 amu + 11.00 amu + 6.15 amu = 41.15 amu

      MCAT CONCEPT CHECK 1.2:

      Before you move on, assess your understanding of the material with these questions.

      What are the definitions of atomic mass and atomic weight?

      Atomic mass: ___________________________________

      Atomic weight: ___________________________________

      While molar mass is typically written in grams per mole (gmol), is the ratio moles per gram (molg) also acceptable?

      _______________________________________

      Calculate and compare the subatomic particles that make up the following atoms.

      1.3 Rutherford, Planck, and Bohr

      LEARNING OBJECTIVES

      After Chapter 1.3, you will be able to:

      Calculate the energy of transition for a valence electron that jumps energy levels

      Calculate the wavelength of an emitted photon given the energy emitted by an electron

      Calculate the energy of a photon given its wavelength

      MCAT EXPERTISE

      The High-Yield badge on this section indicates that the content is frequently tested on the MCAT.

      In 1910, Ernest Rutherford provided experimental evidence that an atom has a dense, positively charged nucleus that accounts for only a small portion of the atom’s volume. Eleven years earlier, Max Planck developed the first quantum theory, proposing that energy emitted as electromagnetic radiation from matter comes in discrete bundles called quanta. The energy of a quantum, he determined, is given by the Planck relation:

      E = hf

      Equation 1.1

      where h is a proportionality constant known as Planck’s constant, equal to 6.626 × 10−34 J · s, and f (sometimes designated by the Greek letter nu, ν) is the frequency of the radiation.

      BRIDGE

      Recall from Chapter 8 of MCAT Physics Review that the speed of light (or any wave) can be calculated using v = fλ. The speed of light, c, is 3 × 10 8   m s . This equation can be incorporated into the equation for quantum energy to provide different derivations.

      Bohr Model

      In 1913, Danish physicist Niels Bohr used the work of Rutherford and Planck to develop his model of the electronic structure of the hydrogen atom. Starting from Rutherford’s findings, Bohr assumed that the hydrogen atom consisted of a central proton around which an electron traveled in a circular orbit. He postulated that the centripetal force acting on the electron as it revolved around the nucleus was created by the electrostatic force between the positively charged proton and the negatively charged electron.

      Bohr used Planck’s quantum theory to correct certain assumptions that classical physics made about the pathways of electrons. Classical mechanics postulates that an object revolving in a circle, such as an electron, may assume an infinite number of values for its radius and velocity. The angular momentum (L = mvr) and kinetic energy ( K = 1 2   m v 2 ) of the object could therefore take on any value. However, by incorporating Planck’s quantum theory into his model, Bohr placed restrictions on the possible values of the angular momentum. Bohr predicted that the possible values for the angular momentum of an electron orbiting a hydrogen nucleus could be given by:

      L = n h 2 π

      Equation 1.2

      where n is the principal quantum number, which can be any positive integer, and h is Planck’s constant. Because the only variable is the principal quantum number, the angular momentum of an electron changes only in discrete amounts with respect to the principal quantum number. Note the similarities between quantized angular momentum and Planck’s concept of quantized energy.

      MCAT EXPERTISE

      When you see a formula in your review or on Test Day, focus on ratios and relationships. This simplifies our calculations to a conceptual understanding, which is usually enough to lead us to the right answer. Further, the MCAT tends to ask how changes in one variable may affect another variable, rather than a plug-and-chug application of complex equations.

      Bohr then related the permitted angular momentum values to the energy of the electron to obtain:

      E = − R H n 2

      Equation 1.3

      where RH is the experimentally determined Rydberg unit of energy, equal to 2.18 × 10 − 18   J electron . Therefore, like angular momentum, the energy of the electron changes in discrete amounts with respect to the quantum number. A value of zero energy was assigned to the state in which the proton and electron are separated completely, meaning that there is no attractive force between them. Therefore, the electron in any of its quantized states in the atom will have an attractive force toward the proton; this is represented by the negative sign in Equation 1.3. Ultimately, the only thing the energy equation is saying is that the energy of an electron increases—becomes less negative—the farther out from the nucleus that it is located (increasing n). This is an important point: while the magnitude of the fraction is getting smaller, the actual value it represents is getting larger (becoming less negative).

      KEY CONCEPT

      At first glance, it may not be clear that the energy (E) is directly proportional to the principal quantum number (n) in Equation 1.3. Take notice of the negative sign, which causes the values to approach zero from a more negative value as n increases (thereby increasing the energy). Negative signs are as important as a variable’s location in a fraction when it comes to determining proportionality.

      Think of the concept of quantized energy as being similar to the change in gravitational potential energy that you experience when you ascend or descend a flight of stairs. Unlike a ramp, on which you could take an infinite number of steps associated with a continuum of potential energy changes, a staircase only allows you certain changes in height and, as a result, allows only certain discrete (quantized) changes of potential energy.

      Bohr came to describe the structure of the hydrogen atom as a nucleus with one proton forming a dense core, around which a single electron revolved in a defined pathway (orbit) at a discrete energy value. If one could transfer an amount of energy exactly equal to the difference between one orbit and another, this could result in the electron jumping from one orbit to a higher-energy one. These orbits had increasing radii, and the orbit with the smallest, lowest-energy radius was defined as the ground state (n = 1). More generally, the ground state of an atom is the state of lowest energy, in which all electrons are in the lowest possible orbitals. In Bohr’s model, the electron was promoted to an orbit with a larger radius (higher energy), the atom was said to be in the excited state. In general, an atom is in an excited state when at least one electron has moved to a subshell of higher than normal energy. Bohr likened his model of the hydrogen atom to the planets orbiting the sun, in which each planet traveled along a roughly circular pathway at set distances—and energy values—from the sun. Bohr’s Nobel Prize-winning model was reconsidered over the next two decades but remains an important conceptualization of atomic behavior. In particular, remember that we now know that electrons are not restricted to specific pathways, but tend to be localized in certain regions of space.

      MCAT EXPERTISE

      Note that all systems tend toward minimal energy; thus on the MCAT, atoms of any element will generally exist in the ground state unless subjected to extremely high temperatures or irradiation.

      Applications of the Bohr Model

      The Bohr model of the hydrogen atom (and other one-electron systems, such as He+ and Li²+) is useful for explaining the atomic emission and absorption spectra of atoms.

      MNEMONIC

      As electrons go from a lower energy level to a higher energy level, they get AHED:

      Absorb light

      Higher potential

      Excited

      Distant (from the nucleus)

      Atomic Emission Spectra

      At room temperature, the majority of atoms in a sample are in the ground state. However, electrons can be excited to higher energy levels by heat or other energy forms to yield excited states. Because the lifetime of an excited state is brief, the electrons will return rapidly to the ground state, resulting in the emission of discrete amounts of energy in the form of photons, as shown in Figure 1.5.

      electron moves from n = 2 to n = 1, emitting energy E = hf

      Figure 1.5. Atomic Emission of a Photon as a Result of a Ground State Transition

      The electromagnetic energy of these photons can be determined using the following equation:

      E = h c λ

      Equation 1.4

      where h is Planck’s constant, c is the speed of light in a vacuum ( 3.00 × 10 8   m s ) , and λ is the wavelength of the radiation. Note that Equation 1.4 is just a combination of two other equations: E = hf and c = f λ.

      The electrons in an atom can be excited to different energy levels. When these electrons return to their ground states, each will emit a photon with a wavelength characteristic of the specific energy transition it undergoes. As described above, these energy transitions do not form a continuum, but rather are quantized to certain values. Thus, the spectrum is composed of light at specified frequencies. It is sometimes called a line spectrum, where each line on the emission spectrum corresponds to a specific electron transition. Because each element can have its electrons excited to a different set of distinct energy levels, each possesses a unique atomic emission spectrum, which can be used as a fingerprint for the element. One particular application of atomic emission spectroscopy is in the analysis of stars and planets: while a physical sample may be impossible to procure, the light from a star can be resolved into its component wavelengths, which are then matched to the known line spectra of the elements as shown in Figure 1.6.

      hydrogen absorption and emission from distant galaxy and background quasar, respectively, and metal absorption lines

      Figure 1.6. Line Spectrum with Transition Wavelengths for Various Celestial Bodies

      REAL WORLD

      Emissions from electrons dropping from an excited state to a ground state give rise to fluorescence. What we see is the color of the emitted light.

      The Bohr model of the hydrogen atom explained the atomic emission spectrum of hydrogen, which is the simplest emission spectrum among all the elements. The group of hydrogen emission lines corresponding to transitions from energy levels n ≥ 2 to n = 1 is known as the Lyman series. The group corresponding to transitions from energy levels n ≥ 3 to n = 2 is known as the Balmer series and includes four wavelengths in the visible region. The Lyman series includes larger energy transitions than the Balmer series; it therefore has shorter photon wavelengths in the UV region of the electromagnetic spectrum. The Paschen series corresponds to transitions from n ≥ 4 to n = 3. These energy transition series can be seen in Figure 1.7.

      Lyman, Balmer, and Paschen series labeled with all transitions between n = 1 and n = 4

      Figure 1.7. Wavelengths of Electron Orbital Transitions

      Energy is inversely proportional to wavelength: E = h f = h c λ .

      The energy associated with a change in the principal quantum number from a higher initial value ni to a lower final value nf is equal to the energy of the photon predicted by Planck’s quantum theory. Combining Bohr’s and Planck’s calculations, we can derive:

      E = h c λ = R H [ 1 n i 2 − 1 n f 2 ]

      Equation 1.5

      This complex-appearing equation essentially says: The energy of the emitted photon corresponds to the difference in energy between the higher-energy initial state and the lower-energy final state.

      KEY CONCEPT

      It may seem strange to see an equation that has initial minus final, where most equations usually have final minus initial. But ultimately, this equation is designed to work just like you'd expect: If an atom emits a photon, the equation gives a negative value for energy, indicating a decrease. You can easily check this for yourself by using ni = 2 and nf = 1.

      Atomic Absorption Spectra

      When an electron is excited to a higher energy level, it must absorb exactly the right amount of energy to make that transition. This means that exciting the electrons of a particular element results in energy absorption at specific wavelengths. Thus, in addition to a unique emission spectrum, every element possesses a characteristic absorption spectrum. Not surprisingly, the wavelengths of absorption correspond exactly to the wavelengths of emission because the difference in energy between levels remains unchanged. Identification of elements in the gas phase requires absorption spectra.

      BRIDGE

      ΔE is the same for absorption or emission between any two energy levels according to the conservation of energy, as discussed in Chapter 2 of MCAT Physics and Math Review. This is also the same as the energy of the photon of light absorbed or emitted.

      Atomic emission and absorption spectra are complex topics, but the takeaway is that each element has a characteristic set of energy levels. For electrons to move from a lower energy level to a higher energy level, they must absorb the right amount of energy to do so. They absorb this energy in the form of light. Similarly, when electrons move from a higher energy level to a lower energy level, they emit the same amount of energy in the form of light.

      REAL WORLD

      Absorption is the basis for the color of compounds. We see the color of the light that is not absorbed by the compound.

      MCAT CONCEPT CHECK 1.3:

      Before you move on, assess your understanding of the material with these questions.

      Note: For these questions, try to estimate the calculations without a calculator to mimic Test Day conditions. Double-check your answers with a calculator and refer to the answers for confirmation of your results.

      The valence electron in a lithium atom jumps from energy level n = 2 to n = 4. What is the energy of this transition in joules? In eV? (Note: RH=2.18×10−18Jelectron=13.6eVelectron)

      _______________________________________

      If an electron emits 3 eV of energy, what is the corresponding wavelength of the emitted photon? (Note: 1 eV = 1.60 × 10−19 J, h = 6.626 × 10−34 J · s)

      _______________________________________

      Calculate the energy of a photon of wavelength 662 nm. (Note: h = 6.626 × 10−34 J · s)

      _______________________________________

      1.4 Quantum Mechanical Model of Atoms

      LEARNING OBJECTIVES

      After Chapter 1.4, you will be able to:

      Identify the four quantum numbers, the potential range of values for each, and their relationship to the electron they represent

      Compare the orbital diagram for a neutral atom, such as sulfur (S), to an ion such as S²–

      Differentiate between paramagnetic and diamagnetic compounds

      Determine the number of valence electrons in a given atom

      While Bohr’s model marked a significant advancement in the understanding of the structure of atoms, his model ultimately proved inadequate to explain the structure and behavior of atoms containing more than one electron. The model’s failure was a result of not taking into account the repulsion between multiple electrons surrounding the nucleus. Modern quantum mechanics has led to a more rigorous and generalizable study of the electronic structure of atoms. The most important difference between Bohr’s model and the modern quantum mechanical model is that Bohr postulated that electrons follow a clearly defined circular pathway or orbit at a fixed distance from the nucleus, whereas modern quantum mechanics has shown that this is not the case. Rather, we now understand that electrons move rapidly and are localized within regions of space around the nucleus called orbitals. The confidence by which those in Bohr’s time believed they could identify the location (or pathway) of the electron was now replaced by a more modest suggestion that the best we can do is describe the probability of finding an electron within a given region of space surrounding the nucleus. In the current quantum mechanical model, it is impossible to pinpoint exactly where an electron is at any given moment in time. This is expressed best by the Heisenberg uncertainty principle: It is impossible to simultaneously determine, with perfect accuracy, the momentum and the position of an electron. If we want to assess the position of an electron, the electron has to stop (thereby removing its momentum); if we want to assess its momentum, the electron has to be moving (thereby changing its position). This can be seen visually in Figure 1.8.

      description given in caption

      Figure 1.8. Heisenberg Uncertainty Principle

      Known momentum and uncertain position (left); known position but uncertain momentum (right). λ = confidence interval of position; px = confidence interval of momentum.

      Quantum Numbers

      Modern atomic theory postulates that any electron in an atom can be completely described by four quantum numbers: n, l, ml, and ms. Furthermore, according to the Pauli exclusion principle, no two electrons in a given atom can possess the same set of four quantum numbers. The position and energy of an electron described by its quantum numbers are known as its energy state. The value of n limits the values of l, which in turn limit the values of ml. In other words, for a given value of n, only particular values of l are permissible; given a value of l, only particular values of ml are permissible. The values of the quantum numbers qualitatively give information about the size, shape, and orientation of the orbitals. As we examine the four quantum numbers more closely, pay attention especially to l and ml because these two tend to give students the greatest difficulty.

      MCAT EXPERTISE

      Think of the quantum numbers as becoming more specific as one goes from n to l to ml to ms. This is like an address: one lives in a particular state (n), in a particular city (l), on a particular street (ml), at a particular house number (ms).

      Principal Quantum Number (n)

      The first quantum number is commonly known as the principal quantum number and is denoted by the letter n. This is the quantum number used in Bohr’s model that can theoretically take on any positive integer value. The larger the integer value of n, the higher the energy level and radius of the electron’s shell. Within each shell, there is a capacity to hold a certain number of electrons, given by:

      Maximum number of electrons within a shell = 2n²

      Equation 1.6

      where n is the principal quantum number. The difference in energy between two shells decreases as the distance from the nucleus increases because the energy difference is a function of [ 1 n i 2 − 1 n f 2 ] . For example, the energy difference between the n = 3 and the n = 4 shells ( 1 9 − 1 16 ) is less than the energy difference between the n = 1 and the n = 2 shells  ( 1 1 − 1 4 ) . This can be seen in Figure 1.7. Remember that electrons do not travel in precisely defined orbits; it just simplifies the visual representation of the electrons’ motion.

      BRIDGE

      Remember, a larger integer value for the principal quantum number indicates a larger radius and higher energy. This is similar to gravitational potential energy, as discussed in Chapter 2 of MCAT Physics Review, where the higher or farther the object is above the Earth, the higher its potential energy will be.

      Azimuthal Quantum Number (l)

      The second quantum number is called the azimuthal (angular momentum) quantum number and is designated by the letter l. The second quantum number refers to the shape and number of subshells within a given principal energy level (shell). The azimuthal quantum number is very important because it has important implications for chemical bonding and bond angles. The value of n limits the value of l in the following way: for any given value of n, the range of possible values for l is 0 to (n – 1). For example, within the first principal energy level, n = 1, the only possible value for l is 0; within the second principal energy level, n = 2, the possible values for l are 0 and 1. A simpler way to remember this relationship is that the n-value also tells you the number of possible subshells. Therefore, there’s only one subshell (l = 0) in the first principal energy level; there are two subshells (l = 0 and 1) within the second principal energy level; there are three subshells (l = 0, 1, and 2) within the third principal energy level, and so on.

      KEY CONCEPT

      For any principal quantum number n, there will be n possible values for l, ranging from 0 to (n – 1).

      Spectroscopic notation refers to the shorthand representation of the principal and azimuthal quantum numbers. The principal quantum number remains a number, but the azimuthal quantum number is designated by a letter: the l = 0 subshell is called s; the l = 1 subshell is called p; the l = 2 subshell is called d; and the l = 3 subshell is called f. Thus, an electron in the shell n = 4 and subshell l = 2 is said to be in the 4d subshell. The spectroscopic notation for each subshell is demonstrated in Figure 1.9.

      periodic table with the periods in each block labeled

      Figure 1.9. Spectroscopic Notation for Every Subshell on the Periodic Table

      Within each subshell, there is a capacity to hold a certain number of electrons, given by:

      Maximum number of electrons within a subshell = 4l + 2

      Equation 1.7

      where l is the azimuthal quantum number. The energies of the subshells increase with increasing l value; however, the energies of subshells from different principal energy levels may overlap. For example, the 4s subshell will have a lower energy than the 3d subshell.

      Figure 1.10 provides an example of computer-generated probability maps of the first few electron clouds in a hydrogen atom. This provides a rough visual representation of the shapes of different subshells.

      s-subshells: circular; p-subshells: bilobed; d-subshells: four-lobed

      Figure 1.10. Electron Clouds of Various Subshells

      Magnetic Quantum Number (ml)

      The third quantum number is the magnetic quantum number and is designated ml. The magnetic quantum number specifies the particular orbital within a subshell where an electron is most likely to be found at a given moment in time. Each orbital can hold a maximum of two electrons. The possible values of ml are the integers between –l and +l, including 0. For example, the s subshell, with l = 0, limits the possible ml values to 0, and because there is a single value of ml, there is only one orbital in the s subshell. The p subshell, with l = 1, limits the possible ml values to −1, 0, and +1, and because there are three values for ml, there are three orbitals in the p subshell. The d subshell has five orbitals (−2 to +2), and the f subshell has seven orbitals (−3 to +3). The shape of the orbitals, like the number of orbitals, is dependent on the subshell in which they are found. The orbitals in the s subshell are spherical, while the three orbitals in the p subshell are each dumbbell-shaped and align along the x-, y-, and z-axes. In fact, the p-orbitals are often referred to as px, py, and pz. The first five orbitals—1s, 2s, 2px, 2py, and 2pz—are demonstrated in Figure 1.11. Note the similarity to the images in Figure 1.10.

      1s: small sphere, 2s: larger sphere; 2px, 2pxy, 2pz: dumbbells aligned with the three axes

      Figure 1.11. The First Five Atomic Orbitals

      KEY CONCEPT

      For any value of l, there will be 2l + 1 possible values for ml. For any n, this produces n² orbitals. For any value of n, there will be a maximum of 2n² electrons (two per orbital).

      The shapes of the orbitals in the d and f subshells are much more complex, and the MCAT will not expect you to answer questions about their appearance. The shapes of orbitals are defined in terms of a concept called probability density, the likelihood that an electron will be found in a particular region of space.

      Take a look at the 2p block in the periodic table. As mentioned above, 2p contains three orbitals. If each orbital can contain two electrons, then six electrons can be added during the course of filling the 2p-orbitals. As atomic number increases, so too does the number of electrons (assuming the species is neutral). Therefore, it should be no surprise that the p block contains six groups of elements. The s block contains two elements in each row of the periodic table, the d block contains ten elements, and the f block contains fourteen elements.

      Spin Quantum Number (ms)

      The fourth quantum number is called the spin quantum number and is denoted by ms. In classical mechanics, an object spinning about its axis has an infinite number of possible values for its angular momentum. However, this does not apply to the electron, which has two spin orientations designated + 1 2 and − 1 2 . Whenever two electrons are in the same orbital, they must have opposite spins. In this case, they are often referred to as being paired. Electrons in different orbitals with the same ms values are said to have parallel spins.

      The quantum numbers for the orbitals in the second principal energy level, with their maximum number of electrons noted in parentheses, are shown in Table 1.2.

      Table 1.2. Quantum Numbers for the Second Principal Energy Level

      Electron Configurations

      For a given atom or ion, the pattern by which subshells are filled, as well as the number of electrons within each principal energy level and subshell, are designated by its electron configuration. Electron configurations use spectroscopic notation, wherein the first number denotes the principal energy level, the letter designates the subshell, and the superscript gives the number of electrons in that subshell. For example, 2p⁴ indicates that there are four electrons in the second (p) subshell of the second principal energy level. This also implies that the energy levels below 2p (that is, 1s and 2s) have already been filled, as shown in Figure 1.12.

      order of subshells: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p

      Figure 1.12. Electron Subshell Flow Diagram

      MCAT EXPERTISE

      Remember that the shorthand used to describe the electron configuration is derived directly from the quantum

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