Chapter 2

Write equations corresponding to the following: a. the fourth ionization energy of Se b. the electron affinity of \(S^{-}\) c. the electron affinity of \(\mathrm{Fe}^{3+}\) d. the ionization energy of \(\mathrm{Mg}\)

Cesium was discovered in natural mineral waters in 1860 by R. W. Bunsen and G. R. Kirchhoff, using the spectroscope they invented in \(1859 .\) The name came from the Latin caesius ("sky blue") because of the prominent blue line observed for this element at \(455.5 \mathrm{nm} .\) Calculate the frequency and energy of a photon of this light.

The bright yellow light emitted by a sodium vapor lamp consists of two emission lines at 589.0 and \(589.6 \mathrm{nm}\). What are the frequency and the energy of a photon of light at each of these wavelengths? What are the energies in \(\mathrm{kJ} / \mathrm{mol} ?\)

Complete and balance the equations for the following reactions. a. \(\mathrm{Li}(s)+\mathrm{N}_{2}(g) \rightarrow\) b. \(\mathrm{Rb}(s)+\mathrm{S}(s) \rightarrow\)

Complete and balance the equations for the following reactions. a. \(\mathrm{Cs}(s)+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow\) b. \(\mathrm{Na}(s)+\mathrm{Cl}_{2}(g) \rightarrow\)

"Lithium" is often prescribed as a mood-stabilizing drug. Do you think the "lithium" prescribed is in the elemental form? What is the more likely form of lithium to be prescribed as a drug?

A carbon-oxygen double bond in a certain organic molecule absorbs radiation that has a frequency of \(6.0 \times 10^{13} \mathrm{s}^{-1}\). a. What is the wavelength of this radiation? b. To what region of the spectrum does this radiation belong? c. What is the energy of this radiation per photon? d. A carbon-oxygen bond in a different molecule absorbs radiation with frequency equal to \(5.4 \times 10^{13} \mathrm{s}^{-1} .\) Is this radiation more or less energetic?

Consider the following approximate visible light spectrum: Barium emits light in the visible region of the spectrum. If each photon of light emitted from barium has an energy of \(3.59 \times 10^{-19} \mathrm{J},\) what color of visible light is emitted?

One of the visible lines in the hydrogen emission spectrum corresponds to the \(n=6\) to \(n=2\) electronic transition. What color light is this transition? See Exercise \(138 .\)

Are the following statements true for the hydrogen atom only, true for all atoms, or not true for any atoms? a. The principal quantum number completely determines the energy of a given electron. b. The angular momentum quantum number, \(\ell,\) determines the shapes of the atomic orbitals. c. The magnetic quantum number, \(m_{\ell},\) determines the direction that the atomic orbitals point in space.

Although no currently known elements contain electrons in \(g\) orbitals in the ground state, it is possible that these elements will be found or that electrons in excited states of known elements could be in \(g\) orbitals. For \(g\) orbitals, the value of \(\ell\) is 4 What is the lowest value of \(n\) for which \(g\) orbitals could exist? What are the possible values of \(m_{\ell} ?\) How many electrons could a set of \(g\) orbitals hold?

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. Excluding hydrogen, which of these elements would have the smallest size? largest size? smallest first ionization energy? largest first ionization energy?

Which of the following orbital designations are incorrect: \(1, s$$1 p, 7 d, 9 s, 3 f, 4 f, 2 d ?\)

The successive ionization energies for an unknown element are \(I_{1}=896 \mathrm{kJ} / \mathrm{mol}\) \(\overline{I_{2}}=1752 \mathrm{kJ} / \mathrm{mol}\) \(I_{3}=14,807 \mathrm{kJ} / \mathrm{mol}\) \(I_{4}=17,948 \mathrm{kJ} / \mathrm{mol}\) To which family in the periodic table does the unknown element most likely belong?

An unknown element is a nonmetal and has a valence electron configuration of \(n s^{2} n p^{4}\). a. How many valence electrons does this element have? b. What are some possible identities for this element? c. What is the formula of the compound this element would form with potassium? d. Would this element have a larger or smaller radius than barium? e. Would this element have a greater or smaller ionization energy than fluorine?

While Mendeleev predicted the existence of several undiscovered elements, he did not predict the existence of the noble gases, the lanthanides, or the actinides. Propose reasons why Mendeleev was not able to predict the existence of the noble gases.

Photosynthesis uses 660 -nm light to convert \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) into glucose and \(\mathrm{O}_{2}\). Calculate the frequency of this light.

Photogray lenses incorporate small amounts of silver chloride in the glass of the lens. When light hits the AgCl particles, the following reaction occurs: $$ \operatorname{AgCl} \stackrel{h v}{\longrightarrow} \mathrm{Ag}+\mathrm{Cl} $$ The silver metal that is formed causes the lenses to darken. The energy change for this reaction is \(3.10 \times 10^{2} \mathrm{kJ} / \mathrm{mol} .\) Assuming all this energy must be supplied by light, what is the maximum wavelength of light that can cause this reaction?

It takes \(476 \mathrm{kJ}\) to remove 1 mole of electrons from the atoms at the surface of a solid metal. How much energy (in kJ) does it take to remove a single electron from an atom at the surface of this solid metal?

Calculate, to four significant figures, the longest and shortest wavelengths of light emitted by electrons in the hydrogen atom that begin in the \(n=5\) state and then fall to states with smaller values of \(n\).

Assume that a hydrogen atom's electron has been excited to the \(n=6\) level. How many different wavelengths of light can be emitted as this excited atom loses energy?

Determine the maximum number of electrons that can have each of the following designations: \(2 f, 2 d_{x y}, 3 p, 5 d_{y z},\) and \(4 p\).

Consider the ground state of arsenic, As. How many electrons have \(\ell=1\) as one of their quantum numbers? How many electrons have \(m_{\ell}=0 ?\) How many electrons have \(m_{\ell}=+1 ?\)

Which of the following statements is(are) true? a. The \(2 s\) orbital in the hydrogen atom is larger than the \(3 s\) orbital also in the hydrogen atom. b. The Bohr model of the hydrogen atom has been found to be incorrect. c. The hydrogen atom has quantized energy levels. d. An orbital is the same as a Bohr orbit. e. The third energy level has three sublevels, the \(s, p,\) and \(d\) sublevels.

Identify the following three elements. a. The ground-state electron configuration is \([\mathrm{Kr}] 5 s^{2} 4 d^{10} 5 p^{4}\). b. The ground-state electron configuration is \([\mathrm{Ar}] 4 s^{2} 3 d^{10} 4 p^{2}\). c. An excited state of this element has the electron configuration \(1 s^{2} 2 s^{2} 2 p^{4} 3 s^{1}\).

Which of the following statements is(are) true? a. F has a larger first ionization energy than does Li. b. Cations are larger than their parent atoms. c. The removal of the first electron from a lithium atom (electron configuration is \(1 s^{2} 2 s^{1}\) ) is exothermic - that is, removing this electron gives off energy. d. The He atom is larger than the \(\mathrm{H}^{+}\) ion. e. The Al atom is smaller than the Li atom.

One of the emission spectral lines for \(\mathrm{Be}^{3+}\) has a wavelength of \(253.4 \mathrm{nm}\) for an electronic transition that begins in the state with \(n=5 .\) What is the principal quantum number of the lower-energy state corresponding to this emission? (Hint: The Bohr model can be applied to one- electron ions. Don't forget the \(Z\) factor: \(Z=\) nuclear charge \(=\) atomic number.

For hydrogen atoms, the wave function for the state \(n=3\) \(\ell=0, m_{\ell}=0\) is $$ \psi_{300}=\frac{1}{81 \sqrt{3 \pi}}\left(\frac{1}{a_{0}}\right)^{3 / 2}\left(27-18 \sigma+2 \sigma^{2}\right) e^{-\sigma \beta} $$ where \(\sigma=r / a_{0}\) and \(a_{0}\) is the Bohr radius \(\left(5.29 \times 10^{-11} \mathrm{m}\right)\) Calculate the position of the nodes for this wave function.

The wave function for the \(2 p_{z}\) orbital in the hydrogen atom is $$ \psi_{2 p_{i}}=\frac{1}{4 \sqrt{2 \pi}}\left(\frac{Z}{a_{0}}\right)^{3 / 2} \sigma \mathrm{e}^{-\alpha / 2} \cos \theta $$ where \(a_{0}\) is the value for the radius of the first Bohr orbit in meters \(\left(5.29 \times 10^{-11}\right), \sigma\) is \(Z\left(r / a_{0}\right), r\) is the value for the distance from the nucleus in meters, and \(\theta\) is an angle. Calculate the value of \(\psi_{2 p^{2}}\) at \(r=a_{0}\) for \(\theta=0^{\circ}\left(z \text { axis) and for } \theta=90^{\circ}\right.\) (xy plane).

Answer the following questions, assuming that \(m_{s}\) could have three values rather than two and that the rules for \(n, \ell,\) and \(m_{\ell}\) are the normal ones. a. How many electrons would an orbital be able to hold? b. How many elements would the first and second periods in the periodic table contain? c. How many elements would be contained in the first transition metal series? d. How many electrons would the set of \(4 f\) orbitals be able to hold?

Assume that we are in another universe with different physical laws. Electrons in this universe are described by four quantum numbers with meanings similar to those we use. We will call these quantum numbers \(p, q, r,\) and \(s .\) The rules for these quantum numbers are as follows: \(p=1,2,3,4,5, \dots\) \(q\) takes on positive odd integers and \(q \leq p\) \(r\) takes on all even integer values from \(-q\) to \(+q\). (Zero is considered an even number.) \(s=+\frac{1}{2}\) or \(-\frac{1}{2}\) a. Sketch what the first four periods of the periodic table will look like in this universe. b. What are the atomic numbers of the first four elements you would expect to be least reactive? c. Give an example, using elements in the first four rows, of ionic compounds with the formulas XY, XY \(_{2}, X_{2} Y, X Y_{3}\) and \(\mathrm{X}_{2} \mathrm{Y}_{3}\) d. How many electrons can have \(p=4, q=3 ?\) e. How many electrons can have \(p=3, q=0, r=0 ?\) f. How many electrons can have \(p=6 ?\)

Without looking at data in the text, sketch a qualitative graph of the third ionization energy versus atomic number for the elements Na through Ar, and explain your graph.

The ionization energy for a \(1 s\) electron in a silver atom is \(2.462 \times 10^{6} \mathrm{kJ} / \mathrm{mol}\) a. Determine an approximate value for \(Z_{\text {eff }}\) for the Ag \(1 s\) electron. Assume the Bohr model applies to the 1 s electron. \(Z_{\mathrm{eff}}\) is the apparent nuclear charge experienced by the electrons. b. How does \(Z_{\text {eff }}\) from part a compare to \(Z\) for Ag? Rationalize the relative numbers.

Answer the following questions based on the given electron configurations and identify the elements. a. Arrange these atoms in order of increasing size: \([\mathrm{Kr}] 5 s^{2} 4 d^{10} 5 p^{6} ;[\mathrm{Kr}] 5 s^{2} 4 d^{10} 5 p^{1} ;[\mathrm{Kr}] 5 s^{2} 4 d^{10} 5 p^{3}\). b. Arrange these atoms in order of decreasing first ionization energy: \([\mathrm{Ne}] 3 s^{2} 3 p^{5} ;[\mathrm{Ar}] 4 s^{2} 3 d^{10} 4 p^{3} ;[\mathrm{Ar}] 4 s^{2} 3 d^{10} 4 p^{5}\).

As the weapons officer aboard the Starship Chemistry, it is your duty to configure a photon torpedo to remove an electron from the outer hull of an enemy vessel. You know that the work function (the binding energy of the electron) of the hull of the enemy ship is \(7.52 \times 10^{-19} \mathrm{J}\) a. What wavelength does your photon torpedo need to be to eject an electron? b. You find an extra photon torpedo with a wavelength of \(259 \mathrm{nm}\) and fire it at the enemy vessel. Does this photon torpedo do any damage to the ship (does it eject an electron)? c. If the hull of the enemy vessel is made of the element with an electron configuration of \([\mathrm{Ar}] 4 s^{1} 3 d^{10},\) what metal is this?