Chapter 7

Ionization energies generally increase with increasing atomic number across the second row of the periodic table, but electron affinities generally decrease. Explain the opposing trends.

Astronomers have detected hydrogen atoms in interstellar space in the \(n=732\) excited state. Suppose an atom in this excited state undergoes a transition from \(n=732\) to \(n=731\) a. How much energy does the atom lose as a result of this transition? b. What is the wavelength of radiation corresponding to this transition? c. What kind of telescope would astronomers need in order to detect radiation of this wavelength? (Hint: It would not be one designed to capture visible light.)

When an atom absorbs an X-ray of sufficient energy, one of its 2 s electrons may be emitted, creating a hole that can be spontaneously filled when an electron in a higher-energy orbital-a \(2 p,\) for example - falls into it. A photon of electromagnetic radiation with an energy that matches the energy lost in the \(2 p \rightarrow 2 s\) transition is emitted. Predict how the wavelengths of \(2 p \rightarrow 2 s\) photons would differ between (a) different elements in the fourth row of the periodic table and (b) different elements in the same column (for example,

A green flame is observed when copper(II) chloride is heated in a flame (Figure \(P 7.129)\) a. Write the ground-state electron configuration for copper atoms. b. There are two common forms of copper chloride, copper(I) chloride and copper(II) chloride. What is the difference in the ground-state electron configurations of copper in these two compounds?

Two helium ions (He') in the \(n=3\) excited state emit photons of radiation as they return to the ground state. One ion does so in a single transition from \(n=3\) to \(n=1 .\) The other does so in two steps: \(n=3\) to \(n=2\) and then \(n=2\) to \(n=1 .\) Which of the following statements about these two pathways is true? a. The sum of the energies lost in the two-step process is the same as the energy lost in the single transition from \(n=3\) to \(n=1\) b. The sum of the wavelengths of the two photons emitted in the two-step process is equal to the wavelength of the single photon emitted in the transition from \(n=3\) to \(n=1\) c. The sum of the frequencies of the two photons emitted in the two-step process is equal to the frequency of the single photon emitted in the transition from \(n=3\) to \(n=1\) d. The wavelength of the photon emitted by the He \(^{+}\) ion in the \(n=3\) to \(n=1\) transition is shorter than the wavelength of a photon emitted by an \(\mathrm{H}\) atom in an \(n=3\) to \(n=1\) transition.

Use your knowledge of electron configurations to explain the following observations: a. Silver tends to form ions with a charge of \(1+\), but the element to the right of silver in the periodic table tends to form ions with \(2+\) charges. b. The heavier group 13 elements (Ga, In, TI) tend to form ions with charges of \(1+\) or \(3+\) but not \(2+\) c. The heavier elements of group \(14(\mathrm{Sn}, \mathrm{Pb})\) and group 4 (Ti, Zr, Hf) tend to form ions with charges of \(2+\) or \(4+\)

Trends in ionization energies of the elements as a function of the position of the elements in the periodic table are a useful test of our understanding of electronic structure. a. Should the same trend in the first ionization energies for elements with atomic numbers \(Z=31\) through \(Z=36\) be observed for the second ionization energies of the same elements? Explain why or why not. b. Which element should have the greater second ionization energy: \(\operatorname{Rb}(Z=37)\) or \(\mathrm{Kr}(Z=36) ?\) Why?

Chemistry of Photo-Gray Glasses "Photo-gray" lenses for eyeglasses darken in bright sunshine because the lenses contain tiny, transparent AgCl crystals. Exposure to light removes electrons from \(\mathrm{Cl}^{-}\) ions, forming a chlorine atom in an excited state (indicated below by the asterisk): $$ \mathrm{Cl}^{-}+b v \rightarrow \mathrm{Cl}^{*}+\mathrm{e}^{-} $$ The electrons are transferred to \(\mathrm{Ag}^{+}\) ions, forming silver metal: $$ \mathrm{Ag}^{+}+\mathrm{e}^{-} \rightarrow \mathrm{Ag} $$ Silver metal is reflective, giving rise to the photo-gray color. a. Write condensed electron configurations of \(\mathrm{Cl}^{-}, \mathrm{Cl}, \mathrm{Ag}\) and \(\mathrm{Ag}^{+}\) b. What do we mean by the term excited state? c. Would more energy be needed to remove an electron from a \(\mathrm{Br}^{-}\) ion or from a \(\mathrm{Cl}^{-}\) ion? Explain your answer. "d. How might substitution of AgBr for AgCl affect the light sensitivity of photo-gray lenses?

The first ionization energy of a gas-phase atom of a particular element is \(6.24 \times 10^{-19} \mathrm{J} .\) What is the maximum wavelength of electromagnetic radiation that could ionize this atom?

Tin (in group 14 ) forms both \(\mathrm{Sn}^{2+}\) and \(\mathrm{Sn}^{4+}\) ions, but magnesium (in group 2 ) forms only \(\mathrm{Mg}^{2+}\) ions. a. Write condensed ground-state electron configurations for the ions \(\mathrm{Sn}^{2+}, \mathrm{Sn}^{4+},\) and \(\mathrm{Mg}^{2+}\) b. Which neutral atoms have ground-state electron configurations identical to \(\mathrm{Sn}^{2+}\) and \(\mathrm{Mg}^{2+} ?\) c. Which \(2^{+}\) ion is isoelectronic with \(\mathrm{Sn}^{4+} ?\)

Between 1999 and 2007 the Far Ultraviolet Spectroscopic Explorer satellite analyzed the spectra of emission sources within the Milky Way. Among the satellite's findings were interplanetary clouds containing oxygen atoms that have lost five electrons. a. Write an electron configuration for these highly ionized oxygen atoms. b. Which electrons have been removed from the neutral atoms? c. The ionization energies corresponding to removal of the third, fourth, and fifth electrons are \(4581 \mathrm{kJ} / \mathrm{mol}$$7465 \mathrm{kJ} / \mathrm{mol},\) and \(9391 \mathrm{kJ} / \mathrm{mol},\) respectively. Explain why removal of each additional electron requires more energy than removal of the previous one. d. What is the maximum wavelength of radiation that will remove the fifth electron from an O atom?

Effective nuclear charge \(\left(Z_{\text {eff }}\right)\) is related to atomic number (Z) by a parameter called the shielding parameter \((\sigma)\) according to the equation \(Z_{\mathrm{eff}}=Z-\sigma\) a. Calculate \(Z_{\mathrm{eff}}\) for the outermost s electrons of Ne and \(\mathrm{Ar}\) given \(\sigma=4.24\) (for \(\mathrm{Ne}\) ) and 11.24 (for \(\mathrm{Ar}\) ). b. Explain why the shielding parameter is much greater for Ar than for Ne.

Sodium fog lamps and street lamps contain gas-phase sodium atoms and sodium ions. Sodium atoms emit yellow-orange light at 589 nm. Do sodium ions emit the same yellow-orange light? Explain why or why not.

How can an electron get from the \((+)\) lobe of a \(p\) orbital to the \((-)\) lobe without going through the node between the lobes?

The wavelengths of Fraunhofer lines in galactic spectra are not exactly the same as those in sunlight: they tend to be shifted to longer wavelengths (redshifted), in part because of the Doppler effect. The Doppler effect is described by the equation $$ \frac{\left(v-v^{\prime}\right)}{v}=\frac{u}{c} $$where \(v\) is the unshifted frequency, \(v^{\prime}\) is the perceived frequency, \(c\) is the speed of light, and \(u\) is the speed at which the object is moving. If hydrogen in a galaxy that is receding from Earth at half the speed of light emits radiation with a wavelength of \(656 \mathrm{nm},\) will the radiation still be in the visible part of the electromagnetic spectrum when it reaches Earth?

The work function of mercury is \(7.22 \times 10^{-19} \mathrm{J}\) a. What is the minimum frequency of radiation required to eject photoelectrons from a mercury surface? b. Could visible light produce the photoelectric effect in mercury?