Chapter 6

A carbon dioxide laser produces radiation of wavelength \(10.6\) micrometers (1 micrometer \(=10^{-6}\) meter). If the laser produces about one joule of energy per pulse, how many photons are produced per pulse?

Name and give the symbol for the element with the characteristic given below: (a) Its electron configuration is \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5}\). (b) Lowest ionization energy in Group 14. (c) Its \(+2\) ion has the configuration \(\left[{ }_{18} \mathrm{Ar}\right] 3 \mathrm{~d}^{5}\). (d) It is the alkali metal with the smallest atomic radius. (e) Largest ionization energy in the fourth period.

Compare the energies and wavelengths of two photons, one with a low frequency, the other with a high frequency.

Consider the following transitions 1\. \(\mathrm{n}=3\) to \(\mathrm{n}=1\) 2\. \(\mathbf{n}=2\) to \(\mathbf{n}=\mathbf{3}\) 3\. \(\mathbf{n}=4\) to \(\mathbf{n}=3\) 4\. \(\mathbf{n}=3\) to \(\mathbf{n}=5\) (a) For which of the transitions is energy absorbed? (b) For which of the transitions is energy emitted? (c) Which transitions involve the ground state? (d) Which transition absorbs the most energy? (e) Which transition emits the most energy?

Write the symbol of each element described below. (a) largest atomic radius in Group 17 (b) smallest atomic radius in period 3 (c) largest first ionization energy in Group 2 (d) most electronegative in Group 16 (e) element(s) in period 2 with no unpaired p electron (f) abbreviated electron configuration is \([\mathrm{Ar}] 4 \mathrm{~s}^{2} 3 \mathrm{~d}^{3}\) (g) A \(+2\) ion with abbreviated electron configuration [Ar] \(3 \mathrm{~d}^{5}\) (h) A transition metal in period 4 forming \(\mathrm{a}+2\) ion with no unpaired electrons

Write the symbol and the abbreviated electron configuration of the element described. (a) the metal in Group 1 whose atom is the smallest (b) the alkaline earth metal with the heaviest atom (c) the transition metal in period 4 whose atom contains the fewest protons (d) the largest metalloid atom with the maximum number of unpaired p electrons (e) an element in period 4 whose \(+2\) ion is isoelectronic with argon

Explain in your own words what is meant by (a) the Pauli exclusion principle. (b) Hund's rule. (c) a line in an atomic spectrum. (d) the principal quantum number.

Explain the difference between (a) the Bohr model of the atom and the quantum mechanical model. (b) wavelength and frequency. (c) the geometries of the three different p orbitals.

Indicate whether each of the following statements is true or false. If false, correct the statement. (a) An electron transition from \(\mathbf{n}=3\) to \(\mathbf{n}=1\) gives off energy. (b) Light emitted by an \(\mathbf{n}=4\) to \(\mathbf{n}=2\) transition will have a longer wavelength than that from an \(\mathbf{n}=5\) to \(\mathbf{n}=2\) transition. (c) A sublevel of \(\ell=3\) has a capacity of ten electrons. (d) An atom of Group 13 has three unpaired electrons.

Criticize or comment on the following statements: (a) The energy of a photon is inversely proportional to its wavelength. (b) The energy of the hydrogen electron is inversely proportional to the quantum number \(\ell\). (c) Electrons start to enter the fifth principal level as soon as the fourth is full.

No currently known elements contain electrons in \(g(\ell=4)\) orbitals in the ground state. If an element is discovered that has electrons in the g or- bital, what is the lowest value for \(\mathbf{n}\) in which these \(\mathrm{g}\) orbitals could exist? What are the possible values of \(\mathbf{m}_{\ell} ?\) How many electrons could a set of \(\mathrm{g}\) orbitals hold?

Indicate whether each of the following is true or false. (a) Effective nuclear charge stays about the same when one goes down a group. (b) Group 17 elements have seven electrons in their outer level. (c) Energy is given off when an electron is removed from an atom.

Explain why (a) negative ions are larger than their corresponding atoms. (b) scandium, a transition metal, forms an ion with a noble-gas structure. (c) electronegativity decreases down a group in the periodic table.

The energy of any one-electron species in its nth state \((\mathbf{n}=\) principal quantum number) is given by \(E=-B Z^{2} / \mathbf{n}^{2}\), where \(Z\) is the charge on the nucleus and \(B\) is \(2.180 \times 10^{-18} \mathrm{~J}\). Find the ionization energy of the \(\mathrm{Li}^{2+}\) ion in its first excited state in kilojoules per mole.

In 1885 , Johann Balmer, a mathematician, derived the following relation for the wavelength of lines in the visible spectrum of hydrogen $$ \lambda=\frac{364.5 \mathrm{n}^{2}}{\left(\mathrm{n}^{2}-4\right)} $$ where \(\lambda\) is in nanometers and \(\mathbf{n}\) is an integer that can be \(3,4,5, \ldots\). Show that this relation follows from the Bohr equation and the equation using the Rydberg constant. Note that in the Balmer series, the electron is returning to the \(\mathbf{n}=2\) level.

Suppose that the spin quantum number could have the values \(\frac{1}{2}, 0\), and \(-\frac{1}{2} .\) Assuming that the rules governing the values of the other quantum numbers and the order of filling sublevels were unchanged, (a) what would be the electron capacity of an s sublevel? A p sublevel? A d sublevel? (b) how many electrons could fit in the \(\mathbf{n}=3\) level? (c) what would be the electron configuration of the element with atomic number 8? \(17 ?\)