Chapter 3

What propertics of an orbital are defined by each of the three quantum numbers \(n, \ell,\) and \(m_{\ell} ?\)

How many quantum numbers are needed to identify an orbital?

How many quantum numbers are needed to identify an electron in an atom?

How many orbitals are there in an atom with each of the following principal quantum numbers? (a) \(1 ;\) (b) \(2 ;\) (c) 3 (d) \(4 ;\) (e) 5.

How many orbitals are there in an atom with the following combinations of quantum numbers? a. \(n=3, e=2\) b. \(n=3, \ell=1\) c. \(n=4, \ell=2, m_{\ell}=2\)

What are the possible values of quantum number \(\ell\) when \(n=4 ?\)

What are the possible values of \(m_{\ell}\) when \(\ell=2 ?\)

Which subshell corresponds to each of the following sets of quantum numbers? a. \(n=6, \ell=0\) b. \(n=3, \ell=2\) c. \(n=2, \ell=1\) d. \(n=5, \ell=4\)

Which subshell corresponds to each of the following sets of quantum numbers? a. \(n=7, \ell=1\) b. \(n=4, \ell=2\) c. \(n=3, \ell=0\) d. \(n=6, \ell=5\)

How many electrons could occupy orbitals with the following quantum numbers? a. \(n=2, \ell=0\) b. \(n=3, \ell=1, m_{\ell}=0\) c. \(n=4, \ell=2\) d. \(n=1, \ell=0, m_{\ell}=0\)

How many electrons could occupy orbitals with the following quantum numbers? a. \(n=3, \ell=2\) b. \(n=5, \ell=4\) c. \(n=3, \ell=0\) d. \(n=4, e=1, m_{\ell}=1\)

Which of the following combinations of quantum numbers are allowed? a. \(n=1, \ell=1, m_{\ell}=0, m_{s}=+\frac{1}{2}\) b. \(n=3, \ell=0, m_{\epsilon}=0, m_{s}=-\frac{1}{2}\) c. \(n=1, \ell=0, m_{\epsilon}=1, m_{s}=-\frac{1}{2}\) d. \(n=2, \ell=1, m_{\epsilon}=2, m_{\mathrm{s}}=+\frac{1}{2}\)

Which of the following combinations of quantum numbers are allowed? a. \(n=3, \ell=2, m_{\ell}=0, m_{\mathrm{s}}=-\frac{1}{2}\) b. \(n=5, \ell=4, m_{\ell}=4, m_{s}=+\frac{1}{2}\) c. \(n=3, \ell=0, m_{\ell}=1, m_{s}=+\frac{1}{2}\) d. \(n=4, \ell=4, m_{\ell}=1, m_{s}=-\frac{1}{2}\)

What is meant when two or more orbitals are said to be degenerate?

Explain how the electron configurations of the group 2 elements are linked to their location in the periodic table.

How do we know from examining the periodic table that the 4 s orbital is filled before the \(3 d\) orbitals?

Why do so many transition metals form ions with a \(2+\) charge?

Identify the subshells with the following combinations of quantum numbers and arrange them in order of increasing energy in a multielectron atom: a. \(n=3, \ell=2\) b. \(n=7, \ell=3\) c. \(n=3, \ell=0\) d. \(n=4, \ell=1\)

Identify the subshells with the following combinations of quantum numbers and arrange them in order of increasine energy in an atom of gold: a. \(n=2, \ell=1\) b. \(n=5, \ell=0\) c. \(n=3, e=2\) d. \(n=4, \ell=3\)

What are the electron configurations of \(\mathrm{Li}^{+}, \mathrm{Ca}, \mathrm{F}^{-}, \mathrm{Mg}^{2+}\) and \(A 1^{3+} ?\)

What are the condensed electron configurations of \(\mathrm{K}, \mathrm{K}^{+}\) \(\mathrm{Ba}, \mathrm{Ti}^{4+}\) and \(\mathrm{Ni} ?\)

How many unpaired electrons are there in the following ground-state atoms and ions? (a) \(\mathrm{N} ;\) (b) \(\mathrm{O} ;\) (c) \(\mathrm{P}^{3-} ;\) (d) \(\mathrm{Na}^{+}\).

How many unpaired electrons are there in the following ground-state atoms and ions? (a) Mn; (b) \(\mathrm{Ag}^{+} ;\) (c) \(\mathrm{Cu}^{3+}\) (d) \(\mathrm{Ti}^{2+}\)

Identify the element whose condensed electron configuration is \([\mathrm{Ne}] 3 s^{2} 3 p^{3} .\) How many unpaired electrons are there in the ground state of this atom?

Which monatomic ion has a charge of \(1-\) and the condensed electron configuration \([\mathrm{Ne}] 3 s^{2} 3 p^{6} ?\) How many unpaired electrons are there in the ground state of this ion?

Which monatomic ion has a charge of \(1+\) and the electron configuration \([\mathrm{Kr}] 4 d^{10} 5 s^{2} ?\) How many unpaired clectrons are there in the ground state of this ion?

Which of the following electron configurations represent an excited state? a. \([\mathrm{He}] 2 s^{1} 2 p^{5}\) b. \(\left[\mathrm{K}_{\mathrm{r}}\right] 4 d^{10} 5 s^{2} 5 p^{1}\) c. \([\mathrm{Ar}] 3 d^{10} 4 s^{2} 4 p^{5}\) d. \([\mathrm{Ne}] 3 s^{2} 3 p^{2} 4 s^{1}\)

Which of the following condensed clectron configurations represent an excited state? Could any represent ground-state clectron configurations of \(2+\) ions? a. \([\mathrm{Ar}] 4 s^{2} 4 p^{1}\) b. \([\mathrm{Ar}] 3 d^{10}\) c. \([\mathrm{Kr}] 4 d^{10} 5 s^{1}\) d. \([\mathrm{Ar}] 3 s^{2} 3 p^{6} 3 d^{1}\)

In which subshell are the highest-energy electrons in a ground-state atom of the isotope \(^{131}\) I? Are the electron configurations of \(^{131} \mathrm{I}\) and \(^{127} \mathrm{I}\) the same?

No known element contains electrons in an \(\ell=4\) subshell in the ground state. If such an element were synthesized, what is the minimum atomic number it would have to have?

Sodium atoms are much larger than chlorine atoms, but sodium ions are much smaller than chloride ions. Why?

Why does atomic size tend to decrease with increasing atomic number across a row of the periodic table?

Using only the periodic table as a guide, arrange each set of particles by size, largest to smallest: a. \(\mathrm{Al}, \mathrm{P}, \mathrm{Cl}, \mathrm{Ar}\) b. \(\mathrm{C}, \mathrm{Si}, \mathrm{Ge}, \mathrm{Sn}\) c. \(\mathrm{Li}^{+}, \mathrm{Li}, \mathrm{Na}, \mathrm{K}\) d. \(F, N e, C 1, C l^{-}\)

Using only the periodic table, arrange each set of particles by size, largest to smallest: a. \(\mathrm{Li}, \mathrm{B}, \mathrm{N}, \mathrm{Ne}\) b. \(\mathrm{Mg}, \mathrm{K}, \mathrm{Ca}, \mathrm{Sr}\) \(\mathrm{c} . \mathrm{Rb}^{+}, \mathrm{Sr}^{2+}, \mathrm{Cs}, \mathrm{Fr}\) \(\mathrm{d} . \mathrm{S}^{2-}, \mathrm{Cl}^{-}, \mathrm{Ar}, \mathrm{K}^{+}\)

How do ionization energies change with increasing atomic number (a) down a group of elements in the periodic table and (b) from left to right across a row?

Explain the differences in ionization energy between (a) He and \(L_{i} ;(b) L i\) and \(B e ;(c)\) Be and \(B ;(d) N\) and \(O\).

How does the wavelength of light required to ionize a gasphase atom change with increasing atomic number down a group in the periodic table?

Why is the first ionization energy of Al less than that of \(\mathrm{Mg}\) and less than that of Si?

Without referring to Figure 3.37 , arrange the following groups of elements in order of increasing first ionization energy. a. \(\mathrm{F}, \mathrm{Cl}, \mathrm{Br}, \mathrm{I}\) b. \(\mathrm{Li}, \mathrm{Be}, \mathrm{Na}, \mathrm{Mg}\) c. \(\mathrm{N}, \mathrm{O}, \mathrm{F}, \mathrm{Ne}\)

Without referring to Figure \(3.37,\) arrange the following groups of elements in order of increasing first ionization energy. a. \(\mathrm{Mg}, \mathrm{Ca}, \mathrm{Sr}, \mathrm{Ba}\) b. \(\mathrm{He}, \mathrm{Ne}, \mathrm{Ar}, \mathrm{Kr}\) c. \(\mathrm{P}, \mathrm{S}, \mathrm{Cl}, \mathrm{Ar}\)

An electron affinity (EA) value that is negative indicates that the free atoms of an element are higher in energy than the \(1-\) anions they form by acquiring electrons. Does this mean that all of the elements with negative EA values exist in nature as anions? Give some examples to support your answer.

The electron affinities of the group 17 elements are all negative values, but the EA values of the group 18 noble gases are all positive. Explain this difference.

The electron affinities of the group 17 elements increase with increasing atomic number. Suggest a reason for this trend.

Ionization energies generally increase with increasing atomic number across the second row of the periodic table, but electron affinities generally decrease. Explain the opposing trends.

Colors of Fireworks Barium compounds are a source of the green colors in many fireworks displays. What is the ground-state electron configuration for \(\mathrm{Ba} ?\) b. The lowest-energy excited state of \(\mathrm{Ba}\) has the electron configuration \([\mathrm{Xe}] 5 d^{1} 6 s^{1} .\) What are the possible quantum numbers \(n, \ell,\) and \(m_{e}\) of a \(5 d\) electron?