Solution: What is the maximum number of electrons that can

What is the relationship between the wavelength of light and the amount of energy carried by its photons? How are wavelength and frequency of light related?

What is light? How fast does light travel?

Explain, in terms of absorbed and reflected light, why a blue object appears blue.

When were the Bohr model and the quantum-mechanical model for the atom developed? What purpose do these models serve?

The quantum-mechanical model, besides revolutionizing chemistry, shook the philosophical world because of its implications regarding determinism. Determinism is the idea that the outcomes of future events are determined by preceding events. The trajectory of a baseball, for example, is deterministic; that is, its trajectory—and therefore its landing place—is determined by its position, speed, and direction of travel. Before quantum mechanics, most scientists thought that fundamental particles—such as electrons and protons—also behaved deterministically. The implication of this belief was that the entire universe must behave deterministically—the future must be determined by preceding events. Quantum mechanics challenged this reasoning because fundamental particles do not behave deterministically—their future paths are not determined by preceding events. Some scientists struggled with this idea. Einstein himself refused to believe it, stating, “God does not play dice with the universe.” Explain what Einstein meant by this statement.

What is white light? Colored light?

List some sources of gamma rays.

How are X-rays used?

Why should excess exposure to gamma rays and X-rays be avoided?

Why should excess exposure to ultraviolet light be avoided?

What objects emit infrared light? What technology exploits this?

Why do microwave ovens heat food, but tend not to heat the dish the food is on?

What type of electromagnetic radiation is used in communications devices such as cellular telephones?

Describe the Bohr model for the hydrogen atom.

Explain the difference between a Bohr orbit and a quantum-mechanical orbital.

What is the difference between the ground state of an atom and an excited state of an atom?

Why do quantum-mechanical orbitals have “fuzzy” boundaries?

What is an emission spectrum? Use the Bohr model to explain why the emission spectrum of the hydrogen atom consists of distinct lines at specific wavelengths.

Explain how the motion of an electron is different from the motion of a baseball. What is a probability map?

List the four possible subshells in the quantum-mechanical model, the number of orbitals in each subshell, and the maximum number of electrons that can be contained in each subshell.

List the quantum-mechanical orbitals through 5s, in the correct energy order for multi-electron atoms.

What is the Pauli exclusion principle? Why is it important when writing electron configurations?

What is Hund’s rule? Why is it important when writing orbital diagrams?

Within an electron configuration, what do symbols such as [Ne] and [Kr] represent?

Explain the difference between valence electrons and core electrons.

Explain why Group 1 elements tend to form 1+ ions and Group 7 elements tend to form 1- ions.

List some examples of the explanatory power of the quantum-mechanical model.

Identify each block in the blank periodic table. (a) \(???? block\) (b) \(???? block\) (c) \(???? block\) (d) \(???? block\) Equation Transcription: Text Transcription: ???? block ???? block ???? block ???? block

Explain the periodic trends in each chemical property. (a) ionization energy (b) atomic size (c) metallic character

How long does it take light to travel in: (a) 1.0 ft (report answer in nanoseconds) (b) 2462 mi, the distance between Los Angeles and New York (report answer in milliseconds) (c) 4.5 billion km, the average separation between the sun and Neptune (report answer in hours and minutes)

How far does light travel in each time period? (a) 1.0 s (b) 1.0 day (c) 1.0 yr

Which type of electromagnetic radiation has the shortest wavelength? (a) radio waves (b) microwaves (c) infrared (d) ultraviolet

Which type of electromagnetic radiation has the longest wavelength? (a) visible (b) ultraviolet (c) infrared (d) X-ray

List the types of electromagnetic radiation in order of increasing energy per photon. (a) radio waves (b) microwaves (c) infrared (d) ultraviolet

List the types of electromagnetic radiation in order of decreasing energy per photon. (a) gamma rays (b) radio waves (c) microwaves (d) visible light

List two types of electromagnetic radiation with frequencies higher than visible light.

List two types of electromagnetic radiation with frequencies lower than infrared light.

List these three types of radiation—infrared, X-ray, and radio waves—in order of: (a) increasing energy per photon (b) increasing frequency (c) increasing wavelength

List these three types of electromagnetic radiation—visible, gamma rays, and microwaves—in order of: (a) decreasing energy per photon (b) decreasing frequency (c) decreasing wavelength

Bohr orbits have fixed ______ and fixed ______.

In the Bohr model, what happens when an electron makes a transition between orbits?

Two of the emission wavelengths in the hydrogen emission spectrum are 410 nm and 434 nm. One of these is due to the n = 6 to n = 2 transition, and the other is due to the n = 5 to n = 2 transition. Which wavelength corresponds to which transition?

Two of the emission wavelengths in the hydrogen emission spectrum are 656 nm and 486 nm. One of these is due to the n = 4 to n = 2 transition, and the other is due to the n = 3 to n = 2 transition. Which wavelength corresponds to which transition?

Sketch the 1s and 2p orbitals. How do the 2s and 3p orbitals differ from the 1s and 2p orbitals?

Sketch the 3d orbitals. How do the 4d orbitals differ from the 3d orbitals?

Which electron is, on average, farther from the nucleus: an electron in a 3p orbital or an electron in a 4p orbital?

According to the quantum-mechanical model for the hydrogen atom, which electron transition produces light with longer wavelength: 2p to 1s or 3p to 1s?

Which electron is, on average, closer to the nucleus: an electron in a 2s orbital or an electron in a 3s orbital?

According to the quantum-mechanical model for the hydrogen atom, which transition produces light with longer wavelength: 3p to 2s or 4p to 2s?

Write full electron configurations for each element. (a) N (b) Mg (c) Ar (d) Se

Write full electron configurations for each element. (a) Sr (b) Ge (c) Li (d) Kr

Write full orbital diagrams and indicate the number of unpaired electrons for each element. (a) F (b) C (c) Ne (d) Be

Write full orbital diagrams and indicate the number of unpaired electrons for each element. (a) He (b) B (c) Li (d) N

Write electron configurations for each element. Use the symbol of the previous noble gas in brackets to represent the core electrons. (a) Ga (b) As (c) Rb (d) Sn

Write electron configurations for each element. Use the symbol of the previous noble gas in brackets to represent the core electrons. (a) Te (b) Br (c) I (d) Cs

Write electron configurations for each transition metal. (a) Zn (b) Cu (c) Zr (d) Fe

Write electron configurations for each transition metal. (a) Mn (b) Ti (c) Cd (d) V

Write full electron configurations and indicate the valence electrons and the core electrons for each element. (a) Kr (b) Ge (c) Cl (d) Sr

Write full electron configurations and indicate the valence electrons and the core electrons for each element. (a) Sb (b) N (c) B (d) K

Write orbital diagrams for the valence electrons and indicate the number of unpaired electrons for each element. (a) Br (b) Kr (c) Na (d) In

Write orbital diagrams for the valence electrons and indicate the number of unpaired electrons for each element. (a) Ne (b) I (c) Sr (d) Ge

How many valence electrons are in each element? (a) O (b) S (c) Br (d) Rb

How many valence electrons are in each element? (a) Ba (b) Al (c) Be (d) Se

List the outer electron configuration for each column in the periodic table. (a) 3A (b) 4A (c) 6A (d) 8A

List the outer electron configuration for each column in the periodic table. (a) 1A (b) 2A (c) 5A (d) 7A

Use the periodic table to write electron configurations for each element. (a) Sr (b) Y (c) Ti (d) Te

Use the periodic table to write electron configurations for each element. (a) Al (b) Be (c) In (d) Zr

Use the periodic table to write electron configurations for each element. (a) Tl (b) Co (c) Ba (d) Sb

How many 2p electrons are in an atom of each element? (a) C (b) N (c) F (d) P

Use the periodic table to write electron configurations for each element. (a) Se (b) Sn (c) Pb (d) Cd

How many 3d electrons are in an atom of each element? (a) Fe (b) Zn (c) K (d) As

List the number of elements in periods 1 and 2 of the periodic table. Why does each period have a different number of elements?

List the number of elements in periods 3 and 4 of the periodic table. Why does each period have a different number of elements?

Name the element in the third period (row) of the periodic table with: (a) 3 valence electrons (b) a total of four 3p electrons (c) six 3p electrons (d) two 3s electrons and no 3p electrons

Name the element in the fourth period of the periodic table with: (a) 5 valence electrons (b) a total of four 4p electrons (c) a total of three 3d electrons (d) a complete outer shell

Use the periodic table to identify the element with each electron configuration. (a) \([N e] 3 s^{2} 3 p^{5}\) (b) \([A r] 4 s^{2} 3 d^{10} 4 p^{1}\) (c) \([A r] 4 s^{2} 3 d^{6}\) (d) \([K r] 5 s^{1}\) Equation Transcription: Text Transcription: [Ne]3s^2 3p^5 [Ar]4s^2 3d^10 4p^1 [Ar]4s^2 3d^6 [Kr]5s^1

Use the periodic table to identify the element with each electron configuration. (a) \([N e] 3 s^{1}\) (b) \([K r] 5 s^{2} 4 d^{10}\) (c) \([X e] 6 s^{2}\) (d) \([K r] 5 s^{2} 4 d^{10} 5 p^{3}\) Equation Transcription: Text Transcription: [Ne]3s^1 [Kr]5s^2 4d^10 [Xe]6s^2 [Kr]5s^2 4d^10 5p^3

Choose the element with the higher ionization energy from each pair. (a) As or Bi (b) As or Br (c) S or I (d) S or Sb

Choose the element with the higher ionization energy from each pair. (a) Al or In (b) Cl or Sb (c) K or Ge (d) S or Se

Arrange the elements in order of increasing ionization energy: Te, Pb, Cl, S, Sn.

Arrange the elements in order of increasing ionization energy: Ga, In, F, Si, N.

Choose the element with the larger atoms from each pair. (a) Sn or Si (b) Br or Ga (c) Sn or Bi (d) Se or Sn

PROBLEM 81P Choose the element with the larger atoms from each pair. (a) Al or In (b) Si or N (c) P or Pb (d) C or F

Arrange these elements in order of increasing atomic size: Cs, Sb, S, Pb, Se.

Arrange these elements in order of increasing atomic size: Ca, Rb, S, Si, Ge, F.

Choose the more metallic element from each pair. (a) Sr or Sb (b) As or Bi (c) Cl or O (d) S or As

Choose the more metallic element from each pair. (a) Sb or Pb (b) K or Ge (c) Ge or Sb (d) As or Sn

Arrange these elements in order of increasing metallic character: Fr, Sb, In, S, Ba, Se.

Arrange these elements in order of increasing metallic character: Sr, N, Si, P, Ga, Al.

Use the electron configurations of the alkaline earth metals to explain why they tend to form 2+ ions.

What is the maximum number of electrons that can occupy the n = 4 quantum shell?

What is the maximum number of electrons that can occupy the n = 3 quantum shell?

Use the electron configuration of oxygen to explain why it tends to form a 2- ion.

Write the electron configuration for each ion. What do all of the electron configurations have in common? (a) \(C a^{2+}\) (b) \(K^{+}\) (c) \(S^{2-}\) (d) \(B r^{-}\) Equation Transcription: Text Transcription: Ca^2+ K^+ S^2- Br^-

Write the electron configuration for each ion. What do all of the electron configurations have in common? (a) \(F^{-}\) (b) \(p^{3-}\) (c) \(L i^{+}\) (d) \(A l^{3+}\) Equation Transcription: Text Transcription: F^- p^3- Li^+ Al^3+

Examine Figure \(4.14\), which shows the elements that form predictable ions. Use what you know about electron configurations to explain these trends. Figure \(4.14\) Elements that form predictable ions Equation Transcription: Text Transcription: 4.14

Examine Figure \(4.12\), which shows the division of the periodic table into metals, nonmetals, and metalloids. Use what you know about electron configurations to explain these divisions. Figure \(4.12\) Metals, nonmetals, and metalloids The elements in the periodic table can be broadly classified as metals, nonmetals, or metalloids. Equation Transcription: Text Transcription: 4.12

Identify what is wrong with each electron configuration and write the correct ground state (or lowest energy) configuration based on the number of electrons. (a) \(1 s^3 2 s^3 2 p^9\) (b) \(1 s^2 2 s^2 2 p^6 2 d^4\) (c) \(1 s^2 1 p^5\) (d) \(1 s^2 2 s^2 2 p^8 3 s^2 3 p^1\)

PROBLEM 98P Identify what is wrong with each electron configuration and write the correct ground state (or lowest energy) configuration based on the number of electrons. (a) 1s42s42p12 (b) 1s22s22p63s23p63d10 (c) 1s22p63s2 (d) 1s22s22p63s23p64s24d104p3

Bromine is a highly reactive liquid, while krypton is an inert gas. Explain this difference based on their electron configurations.

Potassium is a highly reactive metal, while argon is an inert gas. Explain this difference based on their electron configurations.

Based on periodic trends, which one of these elements would you expect to be most easily oxidized: Ge, K, S, or N?

Based on periodic trends, which one of these elements would you expect to be most easily reduced: Ca, Sr, P, or Cl?

When an electron makes a transition from the n = 3 to the n = 2 hydrogen atom Bohr orbit, the energy difference between these two orbits \(\left(3.0 \times 10^{-19} \mathrm{~J}\right)\) is emitted as a photon of light. The relationship between the energy of a photon and its wavelength is given by \(E=h c / \lambda\), where E is the energy of the photon in J, h is Planck’s constant \(\left(6.626 \times 10^{-34} J \cdot s\right)\), and c is the speed of light \(\left(3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)\). Find the wavelength of light emitted by hydrogen atoms when an electron makes this transition.

The distance from the sun to Earth is \(1.496 \times 10^{8} \mathrm{~km}\). How long does it take light to travel from the sun to Earth? Equation Transcription: Text Transcription: 1.496 times 10^8 km

The nearest star is Alpha Centauri, at a distance of 4.3 light-years from Earth. A light-year is the distance that light travels in one year (365 days). How far away, in kilometers, is Alpha Centauri from Earth?

In the beginning of this chapter, you learned that the quantum-mechanical model for the atom is the foundation for modern chemical understanding. Explain why this is so.

Niels Bohr said, “Anyone who is not shocked by quantum mechanics has not understood it.” What do you think he meant by this statement?

The wave nature of matter was first proposed by Louis de Broglie, who suggested that the wavelength \((\lambda)\) of a particle was related to its mass (m) and its velocity (n) by the equation: \(\lambda=h / m v\), where h is Planck’s constant \(\left(6.626 \times 10^{-34} J \cdot s\right)\). Calculate the de Broglie wavelength of: (a) a 0.0459 kg golf ball traveling at 95 m/s; (b) an electron traveling at \(3.88 \times 10^{6} \mathrm{~m} / \mathrm{s}\). Can you explain why the wave nature of matter is significant for the electron but not for the golf ball? (Hint: Express mass in kilograms.) Equation Transcription: Text Transcription: (lambda) lambda = h/mv (6.626 times 10^-34 J cdot s) 3.88 times 10^6 m/s

Excessive exposure to sunlight increases the risk of skin cancer because some of the photons have enough energy to break chemical bonds in biological molecules. These bonds require approximately 250–800 kJ/mol of energy to break. The energy of a single photon is given by ???? = ????????/l, where E is the energy of the photon in J, ???? is Planck’s constant (\(6.626 \times 10^{-34} \mathrm{~J}\)s), and c is the speed of light (\(3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\)). Determine which kinds of light contain enough energy to break chemical bonds in biological molecules by calculating the total energy in 1 mol of photons for light of each wavelength. (a) infrared light (\(1500 nm\)) (b) visible light (\(500 nm\)) (c) ultraviolet light (\(150 nm\)) Equation Transcription: 6.626 10-34J 3.00 × 108 m/s Text Transcription: 6.626 10^-34J 3.00 × 10^8 m/s 1500 nm 500 nm 150 nm

You learned in this chapter that ionization generally increases as you move from left to right across the periodic table. However, consider the data below, which shows the ionization energies of the period 2 and 3 elements: Notice that the increase is not uniform. In fact, ionization energy actually decreases a bit in going from elements in group 2A to 3A and then again from 5A to 6A. Use what you know about electron configurations to explain why these dips in ionization energy exist.

The particle nature of light was first proposed by Albert Einstein, who suggested that light could be described as a stream of particles called photons. A photon of wavelength \(\lambda\) has an energy (E) given by the equation: \(E=h c / \lambda\), where E is the energy of the photon in J, h is Planck’s constant \(\left(6.626 \times 10^{-34} J \cdot s\right)\), and c is the speed of light \(\left(3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)\). Calculate the energy of 1 mol of photons with a wavelength of 632 nm. Equation Transcription: Text Transcription: (lambda) E = hc/lambda (6.626 times 10^-34 J cdot s) (3.00 times 10^8 m/s)

When atoms lose more than one electron, the ionization energy to remove the second electron is always more than the ionization energy to remove the first. Similarly, the ionization energy to remove the third electron is more than the second and so on. However, the increase in ionization energy upon the removal of subsequent electrons is not necessarily uniform. For example, consider the first three ionization energies of magnesium: First ionization energy 738 kJ/mol Second ionization energy 1450 kJ/mol Third ionization energy 7730 kJ/mol The second ionization energy is roughly twice the first ionization energy, but then the third ionization energy is over five times the second. Use the electron configuration of magnesium to explain why this is so. Would you expect the same behavior in sodium? Why or why not?