Chapter 5

A certain minimum energy, \(E_{\text {min }}\) is required to eject an electron from a photosensitive surface. Any energy absorbed beyond this minimum gives kinctic cnergy to the cjected clectron. When \(540 .-\mathrm{nm}\) light falls on a cesium surface, an electron is ejected with a kinctic energy of \(6.69 \times 10^{-20} \mathrm{~J}\). When the wavelength is \(400 \mathrm{nm}\), the kinctic cnergy is \(1.96 \times 10^{-19} \mathrm{~J}\). (a) Calculate \(E_{\text {min }}\) for cesium, in joules. (b) Calculate the longest wavelength, in nanometers, that will eject an electron from cesium.

Suppose a new clement, unbinilium, has recently becn discovered. Its atomic number is 120 . (a) Write the electron configuration of the element. (b) Name another element you would expect to find in the same periodic table group as unhinilium. (c) Write the formulas for the compounds of unbinilium with \(\mathrm{O}\) and \(\mathrm{Cl}\). Use \(\mathrm{X}\) for the chemical symbol.

When sulfur dioxide reacts with chlorine, the products are thionyl chloride, \(\mathrm{SOCl}_{2}\), and dichlorine monoxide, \(\mathrm{OCl}_{2}\) \(\mathrm{SO}_{2}(\mathrm{~g})+2 \mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow \mathrm{SOCl}_{2}(\mathrm{~g})+\mathrm{OCl}_{2}(\mathrm{~g})\) (a) In what period of the periodic table is \(\mathrm{S}\) located? (b) Give the complete electron configuration of \(S\). Do not use the noble-gas notation. (c) \(\Lambda n\) atom of which element involved in this reaction (O. S, or C.1) should have the smallest first ionization energy? The smallest radius? (d) You want to make 675 g \(\mathrm{SOCl}_{2}\). Calculate what mass, in grams, of \(\mathrm{Cl}_{2}\) is required. (e) If you use \(10.0 \mathrm{~g} \mathrm{SO}_{2}\) and \(20.0 \mathrm{~g} \mathrm{Cl}_{2}\), determine the theoretical yield of \(\mathrm{SOCl}_{2}\)

The ionization energy of \(\mathrm{H}(\mathrm{g})\) is \(1312 \mathrm{~kJ} / \mathrm{mol}\). The second ionization energy of \(\mathrm{He}(\mathrm{g})\) is almost exactly four times this value, and the third ionization energy of \(\mathrm{Li}(\mathrm{g})\) is almost exactly nine times that of hydrogen. What relationship, if any, do these data suggest between ionization energy and a fundamental characteristic of elements?

The so-called northern lights (aurora borealis) are caused by ionization and dissociation of \(\mathrm{O}_{2}\) and \(\mathrm{N}_{2}\) molecules through collisions with high-energy electrons ejected from the Sun's surface. Light in the visible region of the electromagnetic spectrum is emitted when the excited ions and atoms return to their ground states. (a) List the emissions in order of increasing energy. (b) Calculate the energy of the photons emitted at \(391.4 \mathrm{nm}\). (c) Give the approximate color of (i) the 557.7 nm emission; (ii) the 470.0 emission. (d) List the species, if any, that are: (i) paramagnetic; (ii) diamagnetic. Explain your choices.

In the upper atmosphere, \(\mathrm{H}-\mathrm{O}\) bonds in water vapor are broken by high-energy photons. To break an \(\mathrm{H}-\mathrm{O}\) bond in water vapor requires an average of \(467 \mathrm{~kJ} / \mathrm{mol}\). (a) Calculate the minimum energy of a photon that can break an \(\mathrm{H}-\mathrm{O}\) bond. (b) From what region of the electromagnetic spectrum does this photon come?

Microwave ovens, commonly used to heat water in bevcrages and foods, cmit radiation with a wavelength of \(12.2 \mathrm{~cm}\) (a) Calculate the amount (moles) of photons of this microwave radiation required to raise the temperature of \(230.0 \mathrm{~g}\) water (such as in a cup of coffee, which is mainly water) from \(24.0^{\circ} \mathrm{C}\) to \(55.0^{\circ} \mathrm{C}\) (b) As noted in Chapter \(4,\) the watt. \(W\), is a unit of power: \(1 \mathrm{~W}=1 \mathrm{~J} / \mathrm{s}\). If the microwave oven is rated at \(800 \mathrm{~W}\) calculate the time needed to heat the water in part (a). Assume that all the energy is delivered to the water.

Use electron configurations to explain why (a) the electron affinity of selenium is lower than that of bromine. (b) the first ionization energy of aluminum is lower than that of magnesium. (c) sulfur has a lower first ionization energy than phosphorus. (d) bromine has a lower first ionization energy than chlorine.

In a hypothetical universe, atoms have two \(s\) orbitals, four \(p\) orbitals, six \(d\) orbitals, and eight \(f\) orbitals. (a) Draw a diagram of the periodic table for this universe, a table that retains the general positions of each block relative to the others. (b) Write the electron configuration for the first \(f\) -block element in this universe.

Write the formula for a compound formed by chlorine and element \(X\), if element \(X\) has the electronic configuration \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{1}\).

Write the formula for a compound formed by potassium and element \(Z,\) if element \(Z\) has the electronic configuration \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{4}\)

Which of these electron configurations are for atoms in the ground state? In excited states? Which are impossible? (a) \(1 s^{2} 2 s^{\prime}\) (b) \(1 s^{2} 2 s^{2} 2 p^{3}\) (c) \([\mathrm{Nc}] 3 s^{2} 3 p^{3} 4 s^{1}\) (d) \([\mathrm{Ne}] 3 s^{2} 3 p^{6} 4 s^{3} 3 d^{2}\) (c) \([\mathrm{Ne}] 3 s^{2} 3 p^{6} 4 f^{4}\) (f) \(1 s^{2} 2 s^{2} 2 p^{4} 3 s^{2}\)

Which of these electron configurations are for atoms in the ground state? In excited states? Which are impossible? (a) \(1 s^{2} 2 s^{2}\) (b) \(1 s^{2} 2 s^{2} 3 s^{1}\) (c) [Ne] \(3 s^{2} 3 p^{8} 4 s^{1}\) (d) \([\mathrm{He}] 2 s^{2} 2 p^{6} 2 d^{2}\) (e) \([\mathrm{Ar}] 4 s^{2} 3 d^{3}\) (f) [Ne] \(3 s^{2} 2 p^{5} 4 s^{1}\)

Use Coulomb's law to predict which substance in each of these pairs has the larger lattice energy. (a) \(\mathrm{CaO}\) or \(\mathrm{Kl}\) (b) \(\mathrm{CaF}_{2}\) or \(\mathrm{BaF}_{2}\) (c) \(\mathrm{KCl}\) or \(\mathrm{LiBr}\)

(a) Calculate the effective nuclear charge, \(Z^{*},\) on a \(2 p\) electron in \(\mathrm{O}^{2-}, \mathrm{F}^{-}, \mathrm{Na}^{+},\) and \(\mathrm{Mg}^{2+}\) (b) Is the calculated effective nuclear charge consistent with the relative sizes of these ions? Explain your answer.

The energy of a photon needed to cause ejection of an electron from a photoemissive metal is expressed as the sum of the binding energy of the photon plus the kinetic energy of the emitted electron. Calculate the kinetic energy of an electron that is emitted from a strontium metal surface irradiated with photons of \(4.20 \times 10^{-7} \mathrm{~m}\) light. The binding energy of strontium is \(4.39 \times 10^{-19} \mathrm{~J}\).

According to a relationship developed by Niels Bohr, for an atom or ion that has a single electron, the total energy of an electron in a stable orbit of quantum number \(n\) is \(E_{n}=-\left[Z^{2} / n^{2}\right]\left(2.179 \times 10^{-18} \mathrm{~J}\right)\) where \(Z\) is the atomic number. Calculate the ionization energy for the electron in a ground-state hydrogen atom.

According to a relationship developed by Niels Bohr, for an atom or ion that has a single electron, the total energy, \(E_{n},\) of an electron in a stable orbit of quantum number \(n\) is \(E_{n}=-\left[Z^{2} / n^{2}\right]\left(2.179 \times 10^{-18} \mathrm{~J}\right)\) where \(Z\) is the atomic number. Calculate the ionization energy for the electron in a ground- state \(\mathrm{He}^{+}\) ion.

Oxygen atoms are smaller than nitrogen atoms, yet oxygen has a lower first ionization energy than nitrogen. Explain. 138\. Beryllium atoms are larger than boron atoms, yet boron has a lower first ionization energy than beryllium. Explain.

Beryllium atoms are larger than boron atoms, yet boron has a lower first ionization energy than beryllium. Explain.

The element meitnerium (Mt) honors Lise Meitner for her role in the discovery of nuclear fission. (a) Meitnerium atoms have the same outer electron configuration as what transition metal? (b) Using the noble-gas notation, write the electron configuration for a ground-state Mt atom.

Suppose two electrons in the same system each have \(n=3, \ell=0\) (a) How many different electron arrangements would be possible if the Pauli exclusion principle did not apply in this case? (b) How many would apply if it is operative?

Only a few atoms of clement 112 , copcrnicium, have ever been synthesized so its chemical propertics are difficult to dctcrminc cxperimentally. (a) The chemical properties of the element ean be expected to be those of what kind of element - main group, transition metal, lanthanide, or actinide'? (b) Using the noble-gas notation, write the electron configuration for a ground-state atom of element 112 to corroborate your answer to part (a).

You are given the atomic radii of \(110 . \mathrm{pm}, 117 \mathrm{pm},\) \(121 \mathrm{pm}, 132 \mathrm{pm}\), and \(153 \mathrm{pm}\), hat do not know to which element (As, Ga, Ge, P, Si) these values correspond. Which must be the value for Ge?