Chapter 6

Exposure to high doses of microwaves can cause tissue damage. Estimate how many photons, with \(\lambda=12 \mathrm{cm},\) must be absorbed to raise the temperature of your eye by \(3.0^{\circ} \mathrm{C}\). Assume the mass of an eye is \(11 \mathrm{g}\) and its specific heat capacity is \(4.0 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}\)

\(.\) The most prominent line in the emission spectrum of chromium is found at \(425.4 \mathrm{nm} .\) Other lines in the chromium spectrum are found at \(357.9 \mathrm{nm}\) \(359.3 \mathrm{nm}, 360.5 \mathrm{nm}, 427.5 \mathrm{nm}, 429.0 \mathrm{nm},\) and \(520.8 \mathrm{nm}\) (a) Which of these lines represents the most energetic light? (b) What color is light of wavelength \(425.4 \mathrm{nm} ?\)

For an electron in a hydrogen atom, calculate the energy of the photon emitted when an electron falls in energy from the \(n=5\) level to the \(n=2\) state. What are the frequency and wavelength of this electromagnetic radiation?

A solution of \(\mathrm{KMnO}_{4}\) absorbs light at \(540 \mathrm{nm}\) (page 206 ). What is the frequency of the light absorbed? What is the energy of one mole of photons with \(\lambda=540 \mathrm{nm} ?\)

Bohr pictured the electrons of the atom as being located in definite orbits about the nucleus, just as the planets orbit the Sun. Criticize this model.

Light is given off by a sodium- or mercury-containing streetlight when the atoms are excited. The light you see arises for which of the following reasons? (a) Electrons are moving from a given energy level to one of higher energy. (b) Electrons are being removed from the atom, thereby creating a metal cation. (c) Electrons are moving from a given energy level to one of lower energy.

What does "wave-particle duality" mean? What are its implications in our modern view of atomic structure?

Which of these are observable? (a) position of an electron in an \(\mathrm{H}\) atom (b) frequency of radiation emitted by \(\mathrm{H}\) atoms (c) path of an electron in an \(\mathrm{H}\) atom (d) wave motion of electrons (e) diffraction patterns produced by electrons (f) diffraction patterns produced by light (g) energy required to remove electrons from \(\mathrm{H}\) atoms (h) an atom (i) a molecule (j) a water wave

In principle, which of the following can be determined? (a) the energy of an electron in the H atom with high precision and accuracy (b) the position of a high-speed electron with high precision and accuracy (c) at the same time, both the position and the energy of a high-speed electron with high precision and accuracy

Suppose you live in a different universe where a different set of quantum numbers is required to describe the atoms of that universe. These quantum numbers have the following rules: \(N,\) principal \(\quad 1,2,3, \ldots, \infty\) \(L,\) orbital \(\quad=N\) \(M,\) magnetic \(\quad-1,0,+1\) How many orbitals are there altogether in the first three electron shells?

Explain why you could or could not measure the wavelength of a golf ball in flight.

The radioactive element technetium is not found naturally on Earth; it must be synthesized in the laboratory. It is a valuable element, however, because it has medical uses. For example, the element in the form of sodium pertechnetate \(\left(\mathrm{NaTcO}_{4}\right)\) is used in imaging studies of the brain, thyroid, and salivary glands and in renal blood flow studies, among other things. (a) In what group and period of the periodic table is the element found? (b) The valence electrons of technetium are found in the \(5 s\) and \(4 d\) subshells. What is a set of quantum numbers \(\left(n, \ell, \text { and } m_{\ell}\right)\) for one of the electrons of the \(5 s\) subshell? (c) Technetium emits a \(\gamma\) -ray with an energy of \(0.141 \mathrm{MeV} .\left(1 \mathrm{MeV}=10^{6}\right.\) electron-volts, where quantum numbers \(\left(n, \ell, \text { and } m_{\ell}\right)\) for one of the electrons of the \(5 s\) subshell? (d) To make \(\mathrm{NaTcO}_{4}\), the metal is dissolved in nitric acid. \begin{aligned} &7 \mathrm{HNO}_{3}(\mathrm{aq})+\mathrm{Tc}(\mathrm{s}) \rightarrow\\\ &&\mathrm{HTcO}_{4}(\mathrm{aq})+7 \mathrm{NO}_{2}(\mathrm{g})+3 \mathrm{H}_{2} \mathrm{O}(\ell) \end{aligned} and the product, \(\mathrm{HTcO}_{4}\) , is treated with \(\mathrm{NaOH}\) to make \(\mathrm{NaTcO}_{4}\) (i) Write a balanced equation for the reaction of (i) Write a balanced equation for the reaction of \(\mathrm{HTCO}_{4}\) with \(\mathrm{NaOH}\). (ii) If you begin with \(4.5 \mathrm{mg}\) of Tc metal, what mass of \(\mathrm{NaTcO}_{4}\) can be made? What mass of \(\mathrm{NaOH}\), in grams, is required to convert all of the \(\mathrm{HTcO}_{4}\) into \(\mathrm{NaTcO}_{4} ?\)