Additional Problems

| 44 | Referring to Figure 30-17 for the order in which the subshells fill and following the style used in Table 30-3, determine the ground- state electronic configuration for cadmium Cd (Z = 48).

| 45 | ssm www In the line spectrum of atomic hydrogen there is also a group of lines known as the Pfund series. These lines are produced when electrons, excited to high energy levels, make transitions to the n = 5 level. Determine (a) the longest wavelength and (b) the shortest wavelength in this series. (c) Refer to Figure 24-10 and identify the region of the electromagnetic spectrum in which these lines are found.

| 46 | The atomic number of lead is Z = 82. According to the Bohr model, what is the energy (in joules) of a X-ray photon?

| 47 | ssm When an electron makes a transition between energy levels of an atom, there are no restrictions on the initial and final values of the principal quantum number n. According to quantum mechanics, however, there is a rule that restricts the initial and final values of the orbital quantum number . This rule is called a selection rule and states that . In other words, when an electron makes a transition between energy levels, the value of can only increase or decrease by one. The value of may not remain the same nor increase or decrease by more than one. According to this rule, which of the following energy level transitions are allowed: (a) 2s → 1s, (b) 2p → 1s, (c) 4p → 2p, (d) 4s → 2p, and (e) 3d → 3s?

| 48 | The characteristic X-ray line for tungsten has a wavelength of . What is the difference in energy between the two energy levels that give rise to this line? Express the answer in (a) joules and (b) electron volts.

| 49 | ssm For a doubly ionized lithium atom Li2+ (Z = 3), what is the principal quantum number of the state in which the electron has the same total energy as a ground-state electron has in the hydrogen atom?

* | 50 | Doubly ionized lithium Li2+ (Z = 3) and triply ionized beryllium Be3+ (Z = 4) each emit a line spectrum. For a certain series of lines in the lithium spectrum, the shortest wavelength is 40.5 nm. For the same series of lines in the beryllium spectrum, what is the shortest wavelength?

* | 51 | The total orbital angular momentum of the electron in a hydrogen atom has a magnitude of . In the quantum mechanical picture of the atom, what values can the angular momentum component Lz have?

* | 52 | Consider a particle of mass m that can exist only between x = 0 m and x = +L on the x axis. We could say that this particle is confined to a “box” of length L. In this situation, imagine the standing de Broglie waves that can fit into the box. For example, the drawing shows the first three possibilities. Note in this picture that there are either one, two, or three half-wavelengths that fit into the distance L. Use Equation 29.8 for the de Broglie wavelength of a particle and derive an expression for the allowed energies (only kinetic energy) that the particle can have. This expression involves m, L, Planck’s constant, and a quantum number n that can have only the values 1, 2, 3,….

* | 53 | ssm The Bohr model can be applied to singly ionized helium He+ (Z = 2). Using this model, consider the series of lines that is produced when the electron makes a transition from higher energy levels into the nf = 4 level. Some of the lines in this series lie in the visible region of the spectrum (380–750 nm). What are the values of ni for the energy levels from which the electron makes the transitions corresponding to these lines?

** | 54 | (a) Derive an expression for the speed of the electron in the nth Bohr orbit, in terms of Z, n, and the constants k, e, and h. For the hydrogen atom, determine the speed in (b) the n = 1 orbit and (c) the n = 2 orbit. (d) Generally, when speeds are less than one-tenth the speed of light, the effects of special relativity can be ignored. Are the speeds found in (b) and (c) consistent with ignoring relativistic effects in the Bohr model?

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