Chapter 6

A photon of violet light has a wavelength of \(423 \mathrm{~nm} .\) Calculate (a) the frequency. (b) the energy in joules per photon. (c) the energy in kilojoules per mole.

Magnetic resonance imaging (MRI) is a powerful diagnostic tool used in medicine. The imagers used in hospitals operate at a frequency of \(4.00 \times 10^{2} \mathrm{MHz}\left(1 \mathrm{MHz}=10^{6} \mathrm{~Hz}\right) .\) Calculate (a) the wavelength. (b) the energy in joules per photon. (c) the energy in kilojoules per mole.

A line in the spectrum of neon has a wavelength of \(837.8 \mathrm{~nm}\). (a) In what spectral range does the absorption occur? (b) Calculate the frequency of this absorption. (c) What is the energy in kilojoules per mole?

The ionization energy of rubidium is \(403 \mathrm{~kJ} / \mathrm{mol}\). Do X-rays with a wavelength of \(85 \mathrm{~nm}\) have sufficient energy to ionize rubidium?

A bar code scanner in a grocery store is a He-Ne laser with a wavelength of \(633 \mathrm{~nm}\). If \(12 \mathrm{~kJ}\) of energy is given off while the scanner is "reading" bar codes, how many photons are emitted?

For the Pfund series, \(\mathbf{n}_{\mathrm{lo}}=5\). (a) Calculate the wavelength in nanometers of a transition from \(\mathbf{n}=7\) to \(\mathrm{n}=5 .\) (b) In what region of the spectrum are these lines formed?

The Brackett series lines in the atomic spectrum of hydrogen result from transitions from \(\mathbf{n}>4\) to \(\mathbf{n}=4\) (a) Calculate the wavelength, in nanometers, of a line in this series resulting from the \(\mathbf{n}=5\) to \(\mathbf{n}=4\) transition. (b) In what region of the spectrum are these lines formed?

In the Paschen series, \(\mathbf{n}_{\text {lo }}=3\). Calculate the longest wavelength possible for a transition in this series.

What are the possible values for \(\mathbf{m}_{\ell}\) for (a) the \(\mathrm{d}\) sublevel? (b) the s sublevel? (c) all sublevels where \(\mathbf{n}=2 ?\)

What are the possible values for \(\mathbf{m}_{\ell}\) for (a) the \(\mathrm{p}\) sublevel? (b) the \(\mathrm{f}\) sublevel? (c) all sublevels where \(\mathbf{n}=3\) ?

For the following pairs of orbitals, indicate which is lower in energy in a many-electron atom. (a) \(3 \mathrm{~d}\) or \(4 \mathrm{~s}\) (b) \(4 \mathrm{f}\) or \(3 \mathrm{~d}\) (c) \(2 \mathrm{~s}\) or \(2 \mathrm{p}\) (d) \(4 \mathrm{f}\) or \(4 \mathrm{~d}\)

For the following pairs of orbitals, indicate which is higher in energy in a many-electron atom. (a) \(3 \mathrm{~s}\) or \(2 \mathrm{p}\) (b) 4 s or \(4 \mathrm{~d}\) (c) \(4 \mathrm{f}\) or \(6 \mathrm{~s}\) (d) 1 s or \(2 \mathrm{~s}\)

What type of electron orbital (i.e., \(\mathrm{s}, \mathrm{p}, \mathrm{d}\), or \(\mathrm{f}\) ) is designated by (a) \(\mathbf{n}=3, \ell=2, \mathbf{m}_{\ell}=-1\) ? (b) \(\mathbf{n}=6, \ell=3, \mathbf{m}_{\ell}=2 ?\) (c) \(\mathbf{n}=4, \ell=3, \mathbf{m}_{\ell}=3\) ?

What type of electron orbital (i.e., s, \(\mathrm{p}, \mathrm{d}\), or \(\mathrm{f}\) ) is designated by (a) \(\mathrm{n}=2, \ell=1, \mathrm{~m}_{\ell}=-1 ?\) (b) \(\mathbf{n}=1, \ell=0, \mathbf{m}_{\ell}=0 ?\) (c) \(\mathrm{n}=5, \ell=2, \mathrm{~m}_{\ell}=2 ?\)

State the total capacity for electrons in (a) \(\mathbf{n}=4\). (b) a 3s sublevel. (c) a d sublevel. (d) a p orbital.

Give the number of orbitals in (a) \(\mathbf{n}=3\). (b) a 4p sublevel. (c) an f sublevel. (d) a d sublevel.

How many electrons in an atom can have each of the following quantum number designations? (a) \(\mathbf{n}=2, \ell=1, \mathbf{m}_{\ell}=0\) (b) \(\mathbf{n}=2, \ell=1, \mathbf{m}_{\ell}=-1\) (c) \(\mathbf{n}=3, \ell=1, \mathbf{m}_{\ell}=0, \mathbf{m}_{s}=+\frac{1}{2}\)

Given the following sets of electron quantum numbers, indicate those that could not occur, and explain your answer. (a) \(3,0,0,-\frac{1}{2}\) (b) \(2,2,1,-\frac{1}{2}\) (c) \(3,2,1,+\frac{1}{2}\) (d) \(3,1,1,+\frac{1}{2}\) (e) \(4,2,-2,0\)

Given the following sets of electron quantum numbers, indicate those that could not occur, and explain your answer. (a) \(3,0,0,-\frac{1}{2}\) (b) \(2,2,1,-\frac{1}{2}\) (c) \(3,2,1,+\frac{1}{2}\) (d) \(3,1,1,+\frac{1}{2}\) (e) \(4,2,-2,0\)

Given the following sets of electron quantum numbers, indicate those that could not occur, and explain your answer. (a) \(1,0,0,-\frac{1}{2}\) (b) \(1,1,0,+\frac{1}{2}\) (c) \(3,2,-2,+\frac{1}{2}\) (d) \(2,1,2,+\frac{1}{2}\) (e) \(4,0,2,+\frac{1}{2}\)

Write the ground state electron configuration for (a) \(\mathrm{N}\) (b) Na (c) Ne (d) Ni (e) Si

Write the ground state electron configuration for (a) \(\mathrm{B}\) (b) \(\mathrm{Ba}\) (c) \(\mathrm{Be}\) (d) \(\mathrm{Bi}\) (e) \(\mathrm{Br}\)

Write the abbreviated ground state electron configuration for (a) \(\mathrm{P}\) (b) As (c) Sn (d) Zr (e) Al

Write the abbreviated ground state electron configuration for (a) Os (b) \(\mathrm{Mg}\) (c) Ge (d) V (e) At

Give the symbol of the element of lowest atomic number whose ground state has (a) a p electron. (b) four felectrons. (c) a completed d subshell. (d) six s electrons.

Give the symbol of the element of lowest atomic number whose ground state has (a) a completed \(\mathrm{f}\) subshell. (b) \(20 \mathrm{p}\) electrons. (c) two \(4 \mathrm{~d}\) electrons. (d) five 5p electrons.

What fraction of the total number of electrons is in d sublevels in (a) C (b) \(\mathrm{Cl}\) (c) Co

What fraction of the total number of electrons is in p sublevels in (a) \(\mathrm{Mg}\) (b) \(\mathrm{Mn}\) (c) Mo

Which of the following electron configurations are for atoms in the ground state? In the excited state? Which are impossible? (a) \(1 s^{2} 2 s^{2} 2 p^{1}\) (b) \(1 s^{2} 1 p^{1} 2 s^{1}\) (c) \(1 s^{2} 2 s^{2} 2 p^{3} 3 s^{1}\) (d) \(1 s^{2} 2 s^{2} 2 p^{6} 3 d^{10}\) (e) \(1 s^{2} 2 s^{2} 2 p^{5} 3 s^{1}\)

Which of the following electron configurations (a-e) are for atoms in the ground state? In the excited state? Which are impossible? (a) \(1 s^{2} 2 p^{1}\) (b) \(1 s^{2} 2 s^{2} 2 p^{4}\) (c) \(1 s^{2} 2 s^{2} 2 p^{5} 3 d^{1}\) (d) \(1 s^{2} 2 s^{2} 2 p^{7} 3 s^{2}\) (e) \(1 s^{2} 2 s^{2} 2 p^{6} 4 s^{1} 3 d^{11}\)

Give the orbital diagram of (a) \(\mathrm{Li}\) (b) \(\mathrm{P}\) (c) \(\mathrm{F}\) (d) Fe

Give the symbols of (a) all the elements in period 2 whose atoms have empty \(2 \mathrm{p}\) orbitals. (b) all the metals in period 3 that have at least one unpaired electron. (c) all the alkaline earth metals that have filled \(3 \mathrm{~d}\) sublevels. (d) all the halogens that have unpaired \(4 p\) electrons.

Give the symbols of (a) all the elements in period 5 that have at least two half-filled \(5 \mathrm{p}\) orbitals. (b) all the elements in Group 1 that have full \(3 \mathrm{p}\) orbitals. (c) all the metalloids that have paired \(3 p\) electrons. (d) all the nonmetals that have full \(3 \mathrm{~d}\) orbitals and 3 half- filled \(3 \mathrm{p}\) orbitals.

Give the number of unpaired electrons in an atom of (a) phosphorus (b) potassium (c) plutonium (Pu)

Give the number of unpaired electrons in an atom of (a) mercury (b) manganese (c) magnesium

In what main group(s) of the periodic table do element(s) have the following number of filled p orbitals in the outermost principal level? (a) 0 (b) 1 (c) 2 (d) 3

Give the symbol of the main-group metals in period 4 with the following number of unpaired electrons per atom. (Transition metals are not included.) (a) 0 (b) 1 (c) 2 (d) 3

Write the ground state electron configuration for (a) \(\mathrm{Mg}, \mathrm{Mg}^{2+}\) (b) \(\mathrm{N}, \mathrm{N}^{3-}\) (c) \(\mathrm{Ti}, \mathrm{Ti}^{4+}\) (d) \(\mathrm{Sn}^{2+}, \mathrm{Sn}^{4+}\)

Write the ground state electron configuration for (a) \(\mathrm{S}, \mathrm{S}^{2-}\) (b) \(\mathrm{Al}, \mathrm{Al}^{3+}\) (c) \(\mathrm{V}, \mathrm{V}^{4+}\) (d) \(\mathrm{Cu}^{+}, \mathrm{Cu}^{2+}\)

How many unpaired electrons are in the following ions? (a) \(\mathrm{Hg}^{2+}\) (b) \(\mathrm{F}^{-}\) (c) \(\mathrm{Sb}^{3+}\) (d) \(\mathrm{Fe}^{3+}\)

How many unpaired electrons are in the following ions? (a) \(\mathrm{Al}^{3+}\) (b) \(\mathrm{Cl}^{-}\) (c) \(\mathrm{Sr}^{2+}\) (d) \(\mathrm{Ag}^{+}\)

Arrange the elements Sr, In, and Te in order of (a) decreasing atomic radius. (b) decreasing first ionization energy. (c) increasing electronegativity.

Arrange the elements Na, Si, and S in order of (a) increasing atomic radius. (b) increasing first ionization energy. (c) decreasing electronegativity.

Which of the four atoms \(\mathrm{Rb}, \mathrm{Sr}, \mathrm{Sb}\), or \(\mathrm{Cs}\) (a) has the smallest atomic radius? (b) has the lowest ionization energy? (c) is the least electronegative?

Which of the four atoms \(\mathrm{Na}, \mathrm{P}, \mathrm{Cl}\), or \(\mathrm{K}\) (a) has the largest atomic radius? (b) has the highest ionization energy? (c) is the most electronegative?

Select the larger member of each pair. (a) \(\mathrm{K}\) and \(\mathrm{K}^{+}\) (b) \(\mathrm{O}\) and \(\mathrm{O}^{2-}\) (c) \(\mathrm{Tl}\) and \(\mathrm{Tl}^{3+}\) (d) \(\mathrm{Cu}^{+}\) and \(\mathrm{Cu}^{2+}\)

Select the smaller member of each pair. (a) \(\mathrm{N}\) and \(\mathrm{N}^{3-}\) (b) \(\mathrm{Ba}\) and \(\mathrm{Ba}^{2+}\) (c) Se and \(\mathrm{Se}^{2-}\) (d) \(\mathrm{Co}^{2+}\) and \(\mathrm{Co}^{3+}\)

List the following species in order of decreasing radius. (a) \(\mathrm{C}, \mathrm{Mg}, \mathrm{Ca}, \mathrm{Si}\) (b) Sr, Cl, Br, I

A lightbulb radiates \(8.5 \%\) of the energy supplied to it as visible light. If the wavelength of the visible light is assumed to be \(565 \mathrm{~nm}\), how many photons per second are emitted by a 75-W lightbulb? \((1 \mathrm{~W}=1 \mathrm{~J} / \mathrm{s})\)

An argon-ion laser is used in some laser light shows. The argon ion has strong emissions at \(485 \mathrm{~nm}\) and \(512 \mathrm{~nm}\). (a) What is the color of these emissions? (b) What is the energy associated with these emissions in kilojoules per mole? (c) Write the ground state electron configuration and orbital diagram of \(\mathrm{Ar}^{+}\).