Chapter 2

Does a photon of visible light \((\lambda=400 \text { to } 700 \mathrm{nm}\) ) have sufficient energy to excite an electron in a hydrogen atom from the \(n=1\) to the \(n=5\) energy state? From the \(n=2\) to the \(n=\) 6 energy state?

An electron is excited from the \(n=1\) ground state to the \(n=\) 3 state in a hydrogen atom. Which of the following statements is/are true? Correct the false statements to make them true. a. It takes more energy to ionize (completely remove) the electron from \(n=3\) than from the ground state. b. The electron is farther from the nucleus on average in the \(n=3\) state than in the \(n=1\) state. c. The wavelength of light emitted if the electron drops from \(n=3\) to \(n=2\) will be shorter than the wavelength of light emitted if the electron falls from \(n=3\) to \(n=1\) d. The wavelcngth of light cmittcd when the clectron returns to the ground state from \(n=3\) will be the same as the wavelength of light absorbed to go from \(n=1\) to \(n=3\) e. For \(n=3,\) the electron is in the first excited state.

Consider an electron for a hydrogen atom in an excited state. The maximum wavelength of electromagnetic radiation that can completely remove (ionize) the electron from the H atom is \(1460 \mathrm{nm}\). What is the initial excited state for the electron \((n=?) ?\)

An excited hydrogen atom with an electron in the \(n=5\) state emits light having a frequency of \(6.90 \times 10^{14} \mathrm{s}^{-1}\). Determine the principal quantum level for the final state in this electronic transition.

An excited hydrogen atom emits light with a wavelength of \(397.2 \mathrm{nm}\) to reach the energy level for which \(n=2 .\) In which principal quantum level did the electron begin?

The Heisenberg uncertainty principle can be expressed in the form $$ \Delta E \cdot \Delta t \geqq \frac{h}{4 \pi} $$ where \(E\) represents energy and \(t\) represents time. Show that the units for this form are the same as the units for the form used in this chapter: $$ \Delta x \cdot \Delta(m v) \geq \frac{h}{4 \pi} $$

What are the possible values for the quantum numbers \(n, \ell\) and \(m_{\ell} ?\)

Which of the following sets of quantum numbers are not allowed in the hydrogen atom? For the sets of quantum numbers that are incorrect, state what is wrong in each set. a. \(n=3, \ell=2, m_{c}=2\) b. \(n=4, \ell=3, m_{\ell}=4\) c. \(n=0, \ell=0, m_{\ell}=0\) d. \(n=2, \ell=-1, m_{c}=1\)

Which of the following sets of quantum numbers are not allowed? For each incorrect set, state why it is incorrect. a. \(n=3, \ell=3, m_{\ell}=0, m_{s}=-\frac{1}{2}\) b. \(n=4, \ell=3, m_{\ell}=2, m_{s}=-\frac{1}{2}\) c. \(n=4, \ell=1, m_{\ell}=1, m_{s}=+\frac{1}{2}\) d. \(n=2, \ell=1, m_{\ell}=-1, m_{s}=-1\) e. \(n=5, \ell=-4, m_{\ell}=2, m_{s}=+\frac{1}{2}\) f. \(n=3, \ell=1, m_{\ell}=2, m_{s}=-\frac{1}{2}\)

What is the physical significance of the value of \(\psi^{2}\) at a particular point in an atomic orbital?

In defining the sizes of orbitals, why must we use an arbitrary value, such as \(90 \%\) of the probability of finding an electron in that region?

How many orbitals in an atom can have the designation \(5 p,\) \(3 d_{z}, 4 d, n=5, n=4 ?\)

How many electrons in an atom can have the designation \(1 p\) \(6 d_{x^{2}-y^{2}}, 4 f, 7 p_{y}, 2 s, n=3 ?\)

Give the maximum number of electrons in an atom that can have these quantum numbers: a. \(n=4\) b. \(n=5, m_{\ell}=+1\) c. \(n=5, m_{s}=+\frac{1}{2}\) d. \(n=3, \ell=2\) e. \(n=2, \ell=1\)

Give the maximum number of electrons in an atom that can have these quantum numbers: a. \(n=0, \ell=0, m_{\ell}=0\) b. \(n=2, \ell=1, m_{\ell}=-1, m_{s}=-\frac{1}{2}\) c. \(n=3, m_{s}=+\frac{1}{2}\) d. \(n=2, \ell=2\) e. \(n=1, \ell=0, m_{\ell}=0\)

Draw atomic orbital diagrams representing the ground-state electron configuration for each of the following elements. a. Na b. Co c. Kr How many unpaired electrons are present in each element?

The elements Si, Ga, As, Ge, Al, Cd, S, and Se are all used in the manufacture of various semiconductor devices. Write the expected electron configuration for these atoms.

The elements \(\mathrm{Cu}, \mathrm{O}, \mathrm{La}, \mathrm{Y}, \mathrm{Ba}, \mathrm{Tl},\) and \(\mathrm{Bi}\) are all found in high-temperature ceramic superconductors. Write the expected electron configuration for these atoms.

Write the expected electron configurations for each of the following atoms: \(\mathrm{Cl}, \mathrm{Sb}, \mathrm{Sr}, \mathrm{W}, \mathrm{Pb}, \mathrm{Cf}\).

The four most abundant elements by mass in the human body are oxygen, carbon, hydrogen, and nitrogen. These four elements make up about \(96 \%\) of the human body. The next four most abundant elements are calcium, phosphorus, magnesium, and potassium. Write the expected ground-state electron configurations for these eight most abundant elements in the human body.

The first-row transition metals from chromium through zinc all have some biologic function in the human body. How many unpaired electrons are present in each of these first-row transition metals in the ground state?

Write the expected ground-state electron configuration for the following. a. the element with one unpaired \(5 p\) electron that forms a covalent compound with fluorine b. the (as yet undiscovered) alkaline earth metal after radium c. the noble gas with electrons occupying \(4 f\) orbitals d. the first-row transition metal with the most unpaired electrons

Given the valence electron orbital level diagram and the description, identify the element or ion. a. A ground state atom b. An atom in an excited state (assume two electrons occupy the \(1 s\) orbital) c. A ground state ion with a charge of -1

Identify the following elements. a. An excited state of this element has the electron configuration \(1 s^{2} 2 s^{2} 2 p^{5} 3 s^{1}\). b. The ground-state electron configuration is \([\mathrm{Ne}] 3 s^{2} 3 p^{4}\). c. An excited state of this element has the electron configuration \([\mathrm{Kr}] 5 s^{2} 4 d^{6} 5 p^{2} 6 s^{1}\). d. The ground-state electron configuration contains three unpaired \(6 p\) electrons.

In the ground state of mercury, Hg, a. how many electrons occupy atomic orbitals with \(n=3 ?\) b. how many electrons occupy \(d\) atomic orbitals? c. how many electrons occupy \(p_{z}\) atomic orbitals? d. how many electrons have spin "up" \(\left(m_{s}=+\frac{1}{2}\right) ?\)

In the ground state of element \(115,\) Uup, a. how many electrons have \(n=5\) as one of their quantum numbers? b. how many electrons have \(\ell=3\) as one of their quantum numbers? c. how many electrons have \(m_{\ell}=1\) as one of their quantum numbers? d. how many electrons have \(m_{s}=-\frac{1}{2}\) as one of their quantum numbers?

Give a possible set of values of the four quantum numbers for all the electrons in a boron atom and a nitrogen atom if each is in the ground state.

Give a possible set of values of the four quantum numbers for the \(4 s\) and \(3 d\) electrons in titanium.

Valence electrons are those electrons in the outermost principal quantum level (highest \(n\) level) of an atom in its ground state. Groups \(1 \mathrm{A}\) to \(8 \mathrm{A}\) have from 1 to 8 valence electrons. For each group of the representative elements (1A-8A), give the number of valence electrons, the general valence electron configuration, a sample element in that group, and the specific valence electron configuration for that element.

How many valence electrons do each of the following elements have, and what are the specific valence electrons for each element? a. Ca b. O c. element 117 d. In e. Ar f. Bi

A certain oxygen atom has the electron configuration \(1 s^{2} 2 s^{2} 2 p_{x}^{2} 2 p_{y}^{2} .\) How many unpaired electrons are present? Is this an excited state of oxygen? In going from this state to the ground state, would energy be released or absorbed?

Which of the following electron configurations correspond to an excited state? Identify the atoms and write the ground-state electron configuration where appropriate. a. \(1 s^{2} 2 s^{2} 3 p^{1}\) b. \(1 s^{2} 2 s^{2} 2 p^{6}\) c. \(1 s^{2} 2 s^{2} 2 p^{4} 3 s^{1}\) d. \([\mathrm{Ar}] 4 s^{2} 3 d^{5} 4 p^{1}\) How many unpaired electrons are present in each of these species?

Which of elements \(1-36\) have two unpaired electrons in the ground state?

One bit of evidence that the quantum mechanical model is "correct" lies in the magnetic properties of matter. Atoms with unpaired electrons are attracted by magnetic fields and thus are said to exhibit paramagnetism. The degree to which this effect is observed is directly related to the number of unpaired electrons present in the atom. Consider the ground-state electron configurations for Li, N, Ni, Te, Ba, and Hg. Which of these atoms would be expected to be paramagnetic, and how many unpaired electrons are present in each paramagnetic atom?

Identify how many unpaired electrons are present in each of the following in the ground state: \(\mathrm{O}, \mathrm{O}^{+}, \mathrm{O}^{-}, \mathrm{Os}, \mathrm{Zr}, \mathrm{S}, \mathrm{F}, \mathrm{Ar}\).

Arrange the following groups of atoms in order of increasing size. a. \(\mathrm{Te}, \mathrm{S}, \mathrm{Se}\) b. \(\mathrm{K}, \mathrm{Br}, \mathrm{Ni}\) c. \(\mathrm{Ba}, \mathrm{Si}, \mathrm{F}\)

In each of the following sets, which atom or ion has the smallest radius? a. \(\mathrm{H}, \mathrm{He}\) b. \(\mathrm{Cl}, \mathrm{In}, \mathrm{Se}\) c. element \(120,\) element \(119,\) element 116 d. \(\mathrm{Nb}, \mathrm{Zn}, \mathrm{Si}\) e. \(\mathrm{Na}^{-}, \mathrm{Na}, \mathrm{Na}^{+}\)

In each of the following sets, which atom or ion has the smallest ionization energy? a. \(\mathrm{Ca}, \mathrm{Sr}, \mathrm{Ba}\) b. \(\mathrm{K}, \mathrm{Mn}, \mathrm{Ga}\) c. \(\mathrm{N}, \mathrm{O}, \mathrm{F}\) d. \(S^{2-}, S, S^{2+}\) e. \(\mathrm{Cs}, \mathrm{Ge}, \mathrm{Ar}\)

Element 106 has been named seaborgium, \(\mathrm{Sg}\), in honor of Glenn Seaborg, discoverer of the first transuranium element. a. Write the expected electron configuration for element 106 b. What other element would be most like element 106 in its properties?

Predict some of the properties of element 117 (the symbol is Uus, following conventions proposed by the International Union of Pure and Applied Chemistry, or IUPAC). a. What will be its electron configuration? b. What element will it most resemble chemically?

The first ionization energies of As and Se are 0.947 and \(0.941 \mathrm{MJ} / \mathrm{mol},\) respectively. Rationalize these values in terms of electron configurations.

Rank the elements Be, B, C, N, and O in order of increasing first ionization energy. Explain your reasoning.

Consider the following ionization energies for aluminum: $$ \begin{aligned} \mathrm{Al}(g) \longrightarrow \mathrm{Al}^{+}(g)+\mathrm{e}^{-} & I_{1}=580 \mathrm{kJ} / \mathrm{mol} \\ \mathrm{Al}^{+}(g) \longrightarrow \mathrm{Al}^{2+}(g)+\mathrm{e}^{-} & I_{2}=1815 \mathrm{kJ} / \mathrm{mol} \\ \mathrm{Al}^{2+}(g) \longrightarrow \mathrm{Al}^{3+}(g)+\mathrm{e}^{-} & I_{3}=2740 \mathrm{kJ} / \mathrm{mol} \\ \mathrm{Al}^{3+}(g) \longrightarrow \mathrm{Al}^{4+}(g)+\mathrm{e}^{-} & I_{4}=11,600 \mathrm{kJ} / \mathrm{mol} \end{aligned} $$ a. Account for the trend in the values of the ionization energies. b. Explain the large increase between \(I_{3}\) and \(I_{4}\).

For each of the following pairs of elements $$ (\mathrm{C} \text { and } \mathrm{N}) \quad(\mathrm{Ar} \text { and } \mathrm{Br}) $$ pick the atom with a. more favorable (more negative) electron affinity. b. higher ionization energy. c. larger size.

For each of the following pairs of elements $$(\mathrm{Mg} \text { and } \mathrm{K}) \quad(\mathrm{F} \text { and } \mathrm{Cl})$$ pick the atom with a. more favorable (more negative) electron affinity. b. higher ionization energy. c. larger size.

The electron affinities of the elements from aluminum to chlorine are \(-44,-120,-74,-200.4,\) and \(-384.7 \mathrm{kJ} / \mathrm{mol},\) respectively. Rationalize the trend in these values.

In the second row of the periodic table, \(\mathrm{Be}, \mathrm{N},\) and \(\mathrm{Ne}\) all have positive (unfavorable) electron affinities, whereas the other second-row elements have negative (favorable) electron affinities. Rationalize why Be, \(N,\) and Ne have unfavorable electron affinities.

Order the atoms in each of the following sets from the least negative electron affinity to the most. a. \(\mathrm{S}, \mathrm{Se}\) b. \(\mathrm{F}, \mathrm{Cl}, \mathrm{Br}, \mathrm{I}\)

The electron affinity for sulfur is more negative than that for oxygen. How do you account for this?

Which has the more negative electron affinity, the oxygen atom or the \(\mathrm{O}^{-}\) ion? Explain your answer.