The MCAT Chemistry Book - Aryangat A. 2012

General Chemistry
Electronic Structure

A. INTRODUCTION

In this chapter, we will discuss the electronic arrangement of atoms. We will also talk about quantum numbers, orbitals, various rules pertaining to electron-filling, and electronic configuration.

B. ATOMIC STRUCTURE

The first ideas about electronic arrangement in atoms were primarily figured out from atomic emission spectra. In various experiments, atoms were made to be thermally or electrically excited, and this resulted in different kinds of bands or lines on photographic plates. Our understanding of atomic structure is based on these types of experiments. All elements have their characteristic line spectra with which they can be analyzed and identified.

Electromagnetic Waves

Before we discuss the atomic structure, we will touch on the topic of electromagnetic radiation to have a better analytical understanding of the key ideas. All electromagnetic radiations travel with a constant speed of 3 x 10⁸ m/s. The electromagnetic spectrum ranges from radio waves to gamma rays.

The Wave Nature

Light has wave nature. It has electric and magnetic fields which are perpendicular to each other, and can travel through space. No medium is required. Because of its wave character, we can define light in terms of frequency and wave length. The distance between two adjacent crests or troughs, or any two adjacent identical points on a wave is called wave length (λ). Frequency (f) is the number of wavelengths passing through a point in unit time. Wavelength and frequency are related by the relation given below. Frequency is usually expressed in 1/second (s^-1), which is otherwise known as hertz (Hz).

The Particle Nature and Quantum Theory

Light has particle nature. These particles or forms (packages) of energy are called quanta. A more modern term for such as particle of light is photon. The energy of a photon can be expressed in terms of the following formula.

According to Heisenberg’s Uncertainty Principle, we cannot determine both the momentum and the position of subatomic particles simultaneously. This is because we are using other particles (electromagnetic particles-like photons) of comparable energy to detect these subatomic particles, and by the time these other particles find the subatomic particles (say electrons), they are also disturbing the pathway of these electrons. In essence, the study of something extremely small and fast (about the magnitude of electrons) cannot be done without interference of its natural course or position.

Photoelectric Effect

The Photoelectric Effect can be defined as the ejection of electrons from a metal surface when light rays strike on it. The ejected electrons are often called “photoelectrons.” The ejection of electrons occurs only if the incident light has a certain minimum or threshold frequency. The required threshold frequency is a characteristic specific to each metal. Experimentally, it has been found that the photoelectrons emitted with maximum energy do not have the full energy equivalent supplied by the incident photon. This is because energy is required to break loose the electrons from the surface of the metal. The energy required for this is called “work function,” which is characteristic of each metal. The photoelectrons can be accelerated to a positively charged plate, creating a flow of charges along a wire-photocurrent. The current can be measured by an ammeter connected to the wire.

The maximum kinetic energy (K_max) of a photoelectron is given by the following equation:

In this equation, m is the mass of an electron, v_maxis the maximum velocity of the electrons, h is the Planck’s constant, f is the frequency of the incident light, φ (pronounced phi) is the “work function” of the metal. The entity hf represents the energy of the incident photon.

Key Observations on Photoelectric Effect

1) The photoelectric effect exemplifies the particle nature of light.

2) Based on conservation of energy, no photoelectron can have energy more than that of an incident photon.

3) The energy of the photoelectrons is always less than that of the incident photons, because some energy (work function) is required to break the electrons loose.

4) The maximum energy of the photoelectrons is independent of the intensity of the incident light.

5) Electrons are not ejected no matter how high the intensity of the incident light is, unless the incident light has the energy corresponding to the threshold frequency characteristic of a particular metal.

Atomic Emission Spectra

When we pass white light through a prism, dispersion of the light occurs resulting in continuous spectrum of wavelengths. Another type of spectrum results when heated gas emits light. This results in a line spectrum. Line spectrum contains only certain specific wavelengths of light. The wavelengths in the visible spectrum of hydrogen is given by the following formula:

where λ is the wavelength of the light, R (Rydberg constant) = 2.18 x 10^—18 J, h (Planck’s constant) = 6.63 x 10^—34 J.s, c (speed of light) = 3.0 x 10⁸ m/s, and n is some whole number that is greater than 2 which corresponds to the orbit-number from which the electron is making the transition. For example, if the transition of an electron is from orbit number 4 to 2, the n value is 4.

Bohr’s Model of Hydrogen Atom

Niel Bohr’s explanation of the hydrogen spectrum was a major breakthrough toward the understanding of atomic structure. The following are the postulates:

1) In each hydrogen atom, the electron revolves around the nucleus in one of the several stable orbits.

2) Each orbit has a definite radius and thus has a definite energy associated with it.

3) An electron in an orbit closest to the nucleus has the lowest energy, and if the electron is in the lowest orbit the atom is said to be in its ground state.

4) The electron in an atom may absorb discrete amounts of energy and move to another orbit with higher energy, and this state is called the excited state.

5) An electron in an excited atom can go back to a lower energy level and this process will result in the release of excess energy as light.

6) The amount of energy released or absorbed is equal to the difference between the energies of the initial and final orbits.

Based on Bohr’s theory, light energy is emitted when an electron in a higher energy level (E_initial) jumps to a lower energy level (E_final). Based on the law of conservation of energy, the sum of energies of the emitted photon (hf) and the electron’s final energy (E_final) should be equal to the electron’s initial energy (E_initial). This can be represented mathematically as follows:

hf + E_final = E_initial

Transitions of the electron in the hydrogen atom result in different spectral lines.

The energy of the emitted photon

where n_final and n_inital are the principal quantum numbers of final and initial energy levels, and R is the Rydberg constant (2.18 x 10^—18 J). The figure given above shows the transitions that can result in the Lyman (ultraviolet region), Balmer (visible region), and Paschen series (infrared region) for nfinal values 1, 2, and 3, respectively.

A photon is emitted when an electron in an atom jumps from a higher to a lower energy level. The energy of the emitted photon is equal to the difference in energy between the two energy levels.

C. QUANTUM NUMBERS

All electrons present in an atom have specific addresses or attributes by which each electron can be referred to. The four quantum numbers are the ones with which we can describe each and every electron that is present in an atom. One of the quantum numbers describes the shape or the most probable area around the nucleus where we can find the particular electrons of interest. This wave function of an electron is called an orbital.

Principal quantum number (n). The principal quantum number denotes the energy level of electrons. The larger the principal quantum number is, the larger the energy. The smaller the principal quantum number is, the lower the energy. The shells are often named K, L, M, N, …, which correspond to the principal quantum numbers 1, 2, 3, 4, …, respectively.

Angular momentum quantum number (l). Angular momentum quantum number (azimuthal quantum number) denotes the shape of the orbital. The values range from 0 to n — 1, where n stands for the principal quantum number. If an electron has a principal quantum number of 4, the values of angular momentum quantum numbers are 0, 1, 2, and 3. The angular momentum quantum numbers correspond to different subshells. An angular momentum quantum number 0 corresponds to s subshell, 1 to p subshell, 2 to d subshell, 3 to f subshell, and so on. For instance, 3d denotes a subshell with quantum numbers n = 3 and l = 2

Magnetic quantum number (m_l). Magnetic quantum numbers define the different spatial orientations of the orbitals. The values from —l to +l. For example, let’s say the value of l is 1. So the magnetic quantum numbers will be —1, 0, and +1. The l value corresponds to p sublevel and the three magnetic quantum numbers correspond to the three atomic orbitals in the p subshell.

Spin quantum number (m_s). Spin quantum number has to do with the spin orientations of an electron. The two possible spins are denoted by the spin quantum numbers +1/2 and —1/2.

D. ELECTRONIC CONFIGURATION

We talked about quantum numbers and atomic orbitals. In this section, we will focus our attention mainly on writing the electronic configuration of atoms and the rules associated with it. First, let’s talk about the ground state electronic configuration. The ground state configuration means the electronic configuration at the lowest energy state.

There are certain rules that should be applied to the filling of orbitals. In order to do that properly, we need to know the Aufbau principle. According to the Aufbau principle, the filling order of electrons obeys a general pattern in which the electrons try to occupy the orbitals in such a way as to minimize the total energy; that is, they occupy the lowest energy orbitals first and then step-by-step go to the next available higher energy levels successively. Of course, there are some exceptions to these generalizations. Some students find it hard to remember the order of filling. The diagram given below may help you. So take a close look. Filling order can be depicted as follows:

This is an easy way to remember the general order of electron-filling in the subshells. The order of filling is 1s, 2s, 2p, 3s, 3p, 4s, 4p, 5s, …, and so on.

An s orbital is spherical in shape. All p orbitals have dumbbell shape with two lobes aligned along an axis (see page 47). All d orbitals have slightly complex shapes (see page 48) and are beyond the scope of our discussion. Each orbital can accommodate a maximum of two electrons. Hence, an s subshell, (only one orbital) can accommodate a maximum of two electrons. Similarly, p (three orbitals), d (five orbitals), and f (seven orbitals) subshells can have maximum of six, ten, and fourteen electrons, respectively.

Table 3-1 Some possible combinations of quantum numbers for atomic orbitals

Example 3-1

Write the electronic configuration of lithium.

Solution: From the periodic table, we can get the atomic number of lithium. The lithium atom has 3 electrons. As we know, 1s subshell is the first one to be filled. The s orbital can hold a maximum of 2 electrons. We have one electron remaining. It will occupy the 2s subshell which is the next energy level. So the third electron will occupy the 2s subshell. Hence, the configuration of lithium is 1s²2s¹.

Example 3-2

Write the electronic configuration of oxygen in its ground state form.

Solution: The oxygen atom contains 8 electrons. The first 2 electrons will go to the 1s level. The next 2 electrons will occupy the 2s level. We have 4 electrons remaining. What is the next subshell according to the filling order? It is 2p. The p subshell can hold a maximum of 6 electrons in its orbitals. So the remaining 4 electrons will occupy the 2p level. Hence, the configuration of oxygen is 1s² 2s² 2p⁴.

Hund’s Rule

We have learned the order of filling the subshells. Now let’s take a closer look at the filling of electrons in an orbital level. Each orbital can be occupied by a maximum of 2 electrons, and these electrons will have opposite spins as dictated by the spin quantum number. Hund’s rule describes the way the electrons fill up the orbitals. According to the Hund’s rule, each electron starts filling up each orbital of a given subshell. After all the orbitals in a given subshell have been filled singly (half-filled), then the electrons start pairing. Let’s look at some examples.

Example 3-3

Write the electronic configuration of sulfur and also show the filling of electrons with orbital notation.

Solution: Sulfur atom has 16 electrons. The electronic configuration is written as 1s² 2s² 2p⁶ 3s² 3p⁴. To see the significance of the Hund’s rule, look at the 3p subshell. In the 3p subshell, we have 3 orbitals.

Note that the electrons first occupy singly in the orbitals. Altogether there are 4 electrons in the 3p subshell. Instead of filling the orbitals in pairs, the first 3 electrons start filling the three orbitals singly, and then the remaining electron occupies the orbital with the other electron as paired electrons. (See the orbital notation of 3p subshell shown above.) If this were not the case, you would have seen two electron-paired orbitals followed by an empty orbital.

Another idea we want to touch on concerns paramagnetic and diamagnetic substances. Substances that have unpaired electrons are called paramagnetic. Substances that have only paired electrons are called diamagnetic.

CHAPTER 3 PRACTICE QUESTIONS

1. Which of the following shows the correct order of filling of subshells?

A. 3s, 3p, 4s, 3d, 4p

B. 3s, 3p, 3d, 4s, 4p

C. 3s, 3d, 3p, 4s, 4p

D. 3s, 3d, 3p, 4p, 4s

2. Which of the following represents the outer most shell configuration of an inert gas?

A. 4s² 4p²

B. 4s² 4p³

C. 4s¹ 4p⁶

D. 4s² 4p⁶

3. The electronic configuration shown below is that of the element:

[Kr] 5s² 4d ¹⁰ 5p²

A. Sb.

B. Rb.

C. In.

D. Sn.

4. The maximum number of electrons that can occupy the energy levels is calculated using a formula, where n represents the number corresponding to the energy level. The formula is:

A. n²

B. 2n²

C. 2n + 1

D. 4n + 2

5. Consider this statement: No two electrons of an atom can have the same sets of four quantum numbers. This is known as the:

A. Heisenberg’s Uncertainty Principle.

B. Hund’s Rule.

C. Pauli Exclusion Principle.

D. Aufbau Principle.

6. Which of the following is true with respect to subshells?

A. The 4p subshell has higher energy than the 5s subshell.

B. The 3p subshell can have a maximum of 3 electrons.

C. The 5d subshell has higher energy than the 6s subshell.

D. The 4f subshell has higher energy than the 5d subshell.

7. Which of the following is NOT isoelectronic with any of the noble gases?

A. Ca²⁺

B. Br ^—

C. S^2—

D. Mg⁺

8. Which of the following is not a possible set of quantum number values for the nitrogen atom, in the order of principal quantum number, azimuthal quantum number, magnetic quantum number, and spin quantum number?

A. 1, 0, 0, — 1/2

B. 2, 1, +1, + 1/2

C. 2, 0, 0, — 1/2

D. 2, 1, +2, + 1/2

9. The electronic configuration [Ar] 3d¹⁰ 4s² 4p² is that of:

A. Ge.

B. Zn.

C. Se.

D. Ar.

10. The electronic configuration of a given element has a 4d subshell. This cannot be the electronic configuration of:

A. Os.

B. Cu.

C. Ag.

D. Ra.