Chapter 6

Cobalt-60 is a radioactive isotope used in medicine for the treatment of certain cancers. It produces \(\beta\) particles and \(\gamma\) rays, the latter having energies of 1.173 and \(1.332 \mathrm{MeV} .\left(1 \mathrm{MeV}=10^{6}\) electron-volts and \right. \(\left.1 \mathrm{eV}=1.6022 \times 10^{-19} \mathrm{J} .\right)\) What are the wavelength and frequency of a \(\gamma\) -ray photon with an energy of 1.173 MeV?

A 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 \(425.4 \mathrm{nm} ?\)

A solution of KMnO absorbs light at 540 nm (page 192). What is the frequency of the light absorbed? What is the energy of one mole of photons with \(\lambda=540 \mathrm{nm} ?\)

A large pickle is attached to two electrodes, which are then attached to a \(110-\mathrm{V}\) power supply. As the voltage is increased across the pickle, it begins to glow with a yellow color. Knowing that pickles are made by soaking the vegetable in a concentrated salt solution, describe why the pickle might emit light when electrical energy is added. (IMAGE CAN'T COPY)

The spectrum shown here is for aspirin. The vertical axis is the amount of light absorbed, and the horizontal axis is the wavelength of incident light (in \(\mathrm{nm}\) ). (For more on spectroscopy, see pages \(183-199 .\) )What is the frequency of light with a wavelength of \(278 \mathrm{nm} ?\) What is the energy of one mole of photons with \(\lambda=278 \mathrm{nm} ?\) What region of the electromagnetic spectrum is covered by the spectrum above? Knowing that aspirin only absorbs light in the region depicted by this spectrum, what is the color of aspirin? (GRAPH CAN'T COPY)

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.

How do we interpret the physical meaning of the square of the wave function? What are the units of \(4 \pi r^{2} \psi^{2} ?\)

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

A 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 \(1,2,3, \ldots, \infty\) \(L,\) 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 \(0.141 \mathrm{MeV} (1 \mathrm{MeV}=10^{6}\) electron-volts, where $$\left.1 \mathrm{eV}=1.6022 \times 10^{-19} \mathrm{J} .\right) \text { What are the wavelength }$$and frequency of a \(\gamma\) -ray photon with an energy of \(0.141 \mathrm{MeV} ?\) (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, HTcO \(_{4}\), is treated with \(\mathrm{NaOH}\) to make \(\mathrm{NaTcO}_{4}\) (i) Write a balanced equation for the reaction of \(\mathrm{HTcO}_{4}\) with \(\mathrm{NaOH}\) (ii) If you begin with 4.5 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 \(\mathrm{NaTcO}_{4} ?\) (e) If you synthesize 1.5 micromoles of \(\mathrm{NaTcO}_{4},\) what mass of compound do you have? If the compound is dissolved in \(10.0 \mathrm{mL}\) of solution, what is the concentration?