Chapter 7

Two objects are moving at the same velocity. Which (if any) of the following statements about them is true? a. The de Broglie wavelength of the heavier object is longer than that of the lighter one. b. If one object has twice as much mass as the other, its wavelength is one- half the wavelength of the other. c. Doubling the velocity of one of the objects will have the same effect on its wavelength as doubling its mass.

Which (if any) of the following statements about the frequency of a particle is true? a. Heavy, fast-moving objects have lower frequencies than those of lighter, faster-moving objects. b. Only very light particles can have high frequencies. c. Doubling the mass of an object and halving its velocity results in no change in its frequency.

How rapidly would each of the following particles be moving if they all had the same wavelength as a photon of red light \((\lambda=750 \mathrm{nm}) ?\) a. an electron of mass \(9.10938 \times 10^{-28} \mathrm{g}\) b. a proton of mass \(1.67262 \times 10^{-24} \mathrm{g}\) c. a neutron of mass \(1.67493 \times 10^{-24} \mathrm{g}\) d. an \(\alpha\) particle of mass \(6.64 \times 10^{-24} \mathrm{g}\)

Kinetic molecular theory tells us that helium atoms at \(500 \mathrm{K}\) are in constant random motion. a. Calculate the root-mean-square speed of helium atoms at \(500 \mathrm{K}\) b. What is the wavelength of a helium atom at \(500 \mathrm{K} ?\)

How does the concept of an orbit in the Bohr model of the hydrogen atom differ from the concept of an orbital in quantum theory?

What properties 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. \(n=3, \ell=2\) 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 \(\ell=2 ?\)

What set of orbitals corresponds to each of the following sets of quantum numbers? How many electrons could occupy these orbitals? a. \(n=2, \ell=0\) b. \(n=3, \ell=1\) c. \(n=4, \ell=2\) d. \(n=1, \ell=0\)

What set of orbitals corresponds to each of the following sets of quantum numbers? How many electrons could occupy these orbitals? a. \(n=2, \ell=1\) b. \(n=5, \ell=3\) c. \(n=3, \ell=2\) d. \(n=4, \ell=3\)

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

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

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

Explain why so many transition metals form ions with a \(2+\) charge.

Why is there only one ground-state electron configuration for an atom but many excited-state electron configurations?

Can the ground-state electron configuration for an atom ever be an excited- state electron configuration for a different atom?

List the following orbitals in order of increasing energy in a multielectron atom: a. \(n=3, \ell=2\) b. \(n=5, \ell=1\) c. \(n=3, \ell=0\) d. \(n=4, \ell=1, m_{\ell}=-1\)

Place the following orbitals in order of increasing energy in a multielectron atom: a. \(n=2, \ell=1\) b. \(n=5, \ell=3\) c. \(n=3, \ell=2\) d. \(n=4, \ell=3\)

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

What are the condensed electron configurations of \(\mathrm{K}, \mathrm{K}^{+}\) \(\mathrm{S}^{2-}, \mathrm{N}, \mathrm{Ba}, \mathrm{Ti}^{4+},\) and \(\mathrm{Al} ?\)

In what way are the electron configurations of \(\mathrm{H}, \mathrm{Li}, \mathrm{Na}, \mathrm{K}\) \(\mathrm{Rb},\) and \(\mathrm{Cs}\) similar?

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) \(\mathrm{Sc} ;\) (b) \(\mathrm{Ag}^{+} ;\) (c) \(\mathrm{Cd}^{2+}\) (d) \(\mathrm{Zr}^{4+}\)

Identify the atom whose electron configuration is \([\mathrm{Ar}] 3 d^{2} 4 s^{2} .\) How many unpaired electrons are there in the ground state of this atom?

Identify the atom whose 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 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 electrons are there in the ground state of this ion?

Does the ground-state electron configuration of \(\mathrm{Na}^{+}\) represent an excited-state electron configuration of Ne?

Predict the charge of the monatomic ions formed by \(\mathrm{Al}\), \(\mathrm{N}\) \(\mathrm{Mg},\) and \(\mathrm{Cs}\)

Predict the charge of the monatomic ions formed by \(\mathrm{S}, \mathrm{P}\) \(\mathrm{Zn},\) and \(\mathrm{I}\)

Which of the following electron configurations represent an excited state? a. \([\mathrm{He}] 2 s^{1} 2 p^{5}\) b. \([\mathrm{Kr}] 4 d^{10} 5 s^{2} 5 p^{1}\) 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 electron configurations represent an excited state? a. \([\mathrm{Ne}] 3 s^{2} 3 p^{1}\) b. \([\mathrm{Ar}] 3 d^{10} 4 s^{1} 4 p^{2}\) c. \([\mathrm{Kr}] 4 d^{10} 5 s^{1} 5 p^{1}\) d. \([\mathrm{Ne}] 3 s^{2} 3 p^{6} 4 s^{1}\)

Introducing calcium chloride into a flame imparts an intense orange color (Figure \(\mathrm{P} 7.110\) ). a. Write ground-state electron configurations for Ca and Cl. b. Calcium chloride contains calcium and chloride ions. Write ground-state electron configurations for each ion.

In which sub-shell 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?

Although no currently known elements contain electrons in \(g\) orbitals \((\ell=4),\) such elements may be synthesized someday. What is the minimum atomic number of an element whose ground-state atoms would have an electron in a \(g\) orbital?

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

Which of the following group 1 elements has the largest atoms: Li, \(\mathrm{Na}, \mathrm{K},\) or \(\mathrm{Rb} ?\) Explain your selection.

Which of the following group 17 elements has the largest monatomic ions: \(\mathrm{F}, \mathrm{Cl}, \mathrm{Br},\) or \(\mathrm{I}\) ? Explain your selection.

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 period of elements?

Explain why it is more difficult to ionize a fluorine atom than a boron atom.

Do you expect the ionization energies of anions of group 17 elements to be lower or higher than for neutral atoms of the same group?

Which of the following elements should have the smallest second ionization energy? \(\mathrm{Br}, \mathrm{Kr}, \mathrm{Rb}, \mathrm{Sr}, \mathrm{Y}\)

Why is the first ionization energy \(\left(\mathrm{IE}_{1}\right)\) of \(\mathrm{Al}(Z=13)\) less than the IE \(_{1}\) of \(\mathrm{Mg}(Z=12)\) and less than the \(\mathrm{IE}_{1}\) of \(\mathrm{Si}\) \((Z=14) ?\)

An electron affinity (EA) value that is negative indicates that the free atoms of an element are less stable 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.