Chapter 1

At the time that J. J. Thomson conducted his experiments on cathode rays, the nature of the electron was in doubt. Some considered it to be a form of radiation, like light; others believed the electron to be a particle. Some of the observations made on cathode rays were used to advance one view or the other. Explain how each of the following properties of cathode rays supports either the wave or the particle model of the electron. (a) They pass through metal foils. (b) They travel at speeds slower than that of light. (c) If an object is placed in their path, they cast a shadow. (d) Their path is deflected when they are passed between electrically charged plates.

Arrange the following types of photons of electromagnetic radiation in order of increasing energy: \(\gamma\)-rays, visible light, ultraviolet radiation, microwaves, \(x\)-rays.

Arrange the following types of photons of electromagnetic radiation in order of increasing frequency: visible light, radio waves, ultraviolet radiation, infrared radiation.

Consider the following statements about electromagnetic radiation and decide whether they are true or false. If they are false, correct them. (a) Photons of ultraviolet radiation have less energy than photons of infrared radiation. (b) The kinetic energy of an electron ejected from a metal surface when the metal is irradiated with ultraviolet radiation is independent of the frequency of the radiation. (c) The energy of a photon is inversely proportional to the wavelength of the radiation.

The \(\gamma\)-ray photons emitted by the nuclear decay of a technetium- 99 atom used in radiopharmaceuticals have an energy of \(140.511 \mathrm{keV}\). Calculate the wavelength of these \(\gamma\)-rays.

A mixture of argon and mercury vapor used in blue advertising signs emits light of wavelength \(470 \mathrm{~nm}\). Calculate the energy change resulting from the emission of \(1.00 \mathrm{~mol}\) of photons at this wavelength.

Sodium vapor lamps, used for public lighting, emit yellow light of wavelength \(589 \mathrm{~nm}\). How much energy is emitted by (a) an excited sodium atom when it generates a photon; (b) \(5.00 \mathrm{mg}\) of sodium atoms emitting light at this wavelength; (c) \(1.00 \mathrm{~mol}\) of sodium atoms emitting light at this wavelength?

When an electron beam strikes a block of copper, x-rays with a frequency of \(1.2 \times 10^{17} \mathrm{~Hz}\) are emitted. How much energy is emitted at this wavelength by (a) an excited copper atom when it generates an \(\mathrm{x}\)-ray photon; (b) \(2.00 \mathrm{~mol}\) of excited copper atoms; (c) \(2.00 \mathrm{~g}\) of copper atoms?

A lamp rated at \(40 \mathrm{~W}\left(1 \mathrm{~W}=1 \mathrm{~J} \cdot \mathrm{s}^{-1}\right)\) emits blue light of wavelength \(470 \mathrm{~nm}\). How many photons of blue light can the lamp generate in \(2.0 \mathrm{~s}\) ?

The energy levels of a particle of mass \(m\) in a twodimensional square box of side \(L\) are given by \(\left(n_{1}^{2}+n_{2}^{2}\right) h^{2} / 8 m L^{2}\). Are any of the levels degenerate? If so, find the values of the quantum numbers \(n_{1}\) and \(n_{2}\) for which these degeneracies arise for the first three cases.

(a) Using the particle-in-the-box model for the hydrogen atom and treating the atom as electron in a one-dimensional box of length 150 . pm, predict the wavelength of radiation emitted when the electron falls from the level with \(n=3\) to that with \(n=2\). (b) Repeat the calculation for the transition from \(n=4\) to \(n=2\).

(a) What is the highest energy photon that can be absorbed by a ground-state hydrogen atom without causing ionization? (b) What is the wavelength of this radiation? (c) To what region of the electromagnetic spectrum does this photon belong?

Show that the electron distribution is spherically symmetrical for an atom in which an electron occupies each of the three p-orbitals of a given shell.

At what distance from the nucleus is the electron most likely to be found if it occupies (a) a 3d-orbital or (b) a 4s-orbital in a hydrogen atom?

(a) Sketch the shape of the boundary surfaces corresponding to \(1 \mathrm{~s}-, 2 \mathrm{p}-\), and \(3 \mathrm{~d}\)-orbitals. (b) What is meant by a node? (c) How many radial nodes and angular nodal surfaces does each orbital have? (d) Predict the number of nodal planes expected for a \(4 \mathrm{f}\)-orbital.

Locate the positions of the radial nodes of (a) a \(3 \mathrm{~s}\)-orbital; (b) a 4d-orbital.

Describe the orientation of the lobes of the \(\mathrm{p}_{x^{-}}, \mathrm{p}_{y^{-}}\), and \(\mathrm{p}_{z}\)-orbitals with respect to the reference Cartesian axes.

How many orbitals are in subshells with \(l\) equal to (a) 0 ; (b) 2 ; (c) 1 ; (d) 3?

(a) How many subshells are there for principal quantum number \(n=5\) ? (b) Identify the subshells in the form \(5 \mathrm{~s}\), etc. (c) How many orbitals are there in the shell with \(n=5\) ?

(a) How many values of the quantum number \(l\) are possible when \(n=7\) ? (b) How many values of \(m_{l}\) are allowed for an electron in a \(6 \mathrm{~d}\)-subshell? (c) How many values of \(m_{l}\) are allowed for an electron in a \(3 \mathrm{p}\)-subshell? (d) How many subshells are there in the shell with \(n=4\) ?

(a) How many values of the quantum number \(l\) are possible when \(n=6\) ? (b) How many values of \(m_{l}\) are allowed for an electron in a \(5 \mathrm{f}\)-subshell? (c) How many values of \(m_{l}\) are allowed for an electron in a 2 s-subshell? (d) How many subshells are there in the shell with \(n=3\) ?

What are the principal and orbital angular momentum quantum numbers for each of the following orbitals: (a) 6p; (b) \(3 \mathrm{~d}\); (c) \(2 \mathrm{p}\); (d) \(5 \mathrm{f}\) ?

What are the principal and orbital angular momentum quantum numbers for each of the following orbitals: (a) \(2 \mathrm{~s}\); (b) \(6 \mathrm{f}\); (c) 4d; (d) \(5 \mathrm{p}\) ?

How many electrons can occupy (a) the 4p-orbitals? (b) the \(3 \mathrm{~d}\)-orbitals? (c) the \(1 \mathrm{~s}\)-orbital? (d) the \(4 \mathrm{f}\)-orbitals?

How many electrons can occupy a subshell with \(l=\) (a) 0 ; (b) \(1 ;\) (c) \(2 ;\) (d) 3 ?

1.59 Write the subshell notation (3d, for instance) and the number of orbitals having the following quantum numbers: (a) \(n=5\), \(l=2\); (b) \(n=1, l=0\); (c) \(n=6, l=3\); (d) \(n=2, l=1\).

Write the subshell notation (3d, for instance) and the number of electrons that can have the following quantum numbers if all the orbitals of that subshell are filled: (a) \(n=4, l=1\); (b) \(n=5\), \(l=0 ;\) (c) \(n=6, l=2 ;\) (d) \(n=7, l=3\).

How many electrons can have the following quantum numbers in an atom: (a) \(n=2, l=1\); (b) \(n=4, l=2, m_{l}=-2\); (c) \(n=2\); (d) \(n=3, l=2, m_{l}=+1\) ?

How many electrons can have the following quantum numbers in an atom: (a) \(n=3, l=1\); (b) \(n=5, l=3, m_{l}=-1\); (c) \(n=2, l=1, m_{l}=0\); (d) \(n=7\) ?

Which of the following subshells cannot exist in an atom: (a) \(2 \mathrm{~d}\); (b) \(4 \mathrm{~d}\); (c) \(4 \mathrm{~g}\); (d) \(6 \mathrm{f}\) ?

Which of the following subshells cannot exist in an atom: (a) \(4 \mathrm{f}\); (b) \(3 \mathrm{f}\); (c) \(5 \mathrm{~g}\); (d) \(6 \mathrm{~h}\) ?

Which of the following statements are true for many-electron atoms? If false, explain why. (a) The effective nuclear charge \(Z_{\text {eff }}\) is independent of the number of electrons present in an atom. (b) Electrons in an s-orbital are more effective than those in other orbitals at shielding other electrons from the nuclear charge because an electron in an \(s\)-orbital can penetrate to the nucleus of the atom. (c) Electrons having \(l=2\) are better at shielding than electrons having \(l=1\). (d) \(Z_{\text {eff }}\) for an electron in a p-orbital is lower than for an electron in an \(s\)-orbital in the same shell.

For the electrons on a carbon atom in the ground state, decide which of the following statements are true. If false, explain why. (a) \(Z_{\text {eff }}\) for an electron in a 1s-orbital is the same as \(Z_{\text {eff }}\) for an electron in a \(2 \mathrm{~s}\)-orbital. (b) \(Z_{\text {eff }}\) for an electron in a \(2 \mathrm{~s}\)-orbital is the same as \(Z_{\text {eff }}\) for an electron in a 2p-orbital. (c) An electron in the \(2 \mathrm{~s}\)-orbital has the same energy as an electron in the \(2 \mathrm{p}\)-orbital. (d) The electrons in the \(2 \mathrm{p}\)-orbitals have spin quantum numbers \(m_{s}\) of opposite sign. (e) The electrons in the \(2 \mathrm{~s}\)-orbital have the same value of the quantum number \(m_{s}\).

Of the following sets of four quantum numbers \(\left\\{n, l, m_{l}, m_{s}\right\\}\), identify the ones that are forbidden for an electron in an atom and explain why they are invalid: (a) \(\left\\{4,2,-1,+\frac{1}{2}\right\\}\); (b) \(\left\\{5,0,-1,+\frac{1}{2}\right\\}\); (c) \(\left\\{4,4,-1,+\frac{1}{2}\right\\}\).

Of the following sets of four quantum numbers \(\left\\{n, l, m_{l}, m_{s}\right\\}\), identify the ones that are forbidden for an electron in an atom and explain why they are invalid: (a) \(\left\\{2,2,-1,+\frac{1}{2}\right\\} ;\) (b) \(\left\\{6,6,0,+\frac{1}{2}\right\\} ;\) (c) \(\left\\{5,4,+5,+\frac{1}{2}\right\\}\)

What is the ground-state electron configuration expected for each of the following elements: (a) silver; (b) beryllium; (c) antimony; (d) gallium; (e) tungsten; (f) iodine?

What is the ground-state electron configuration expected for each of the following elements: (a) arsenic; (b) strontium; (c) tin; (d) platinum; (e) osmium; (f) molybdenum?

Which elements are predicted to have the following groundstate electron configurations: (a) \([\mathrm{Kr}] 4 \mathrm{~d}^{10} 5 \mathrm{~s}^{2} 5 \mathrm{p}^{4} ;\) (b) \([\mathrm{Ar}] 3 \mathrm{~d}^{3} 4 \mathrm{~s}^{2}\); (c) \([\mathrm{He}] 2 \mathrm{~s}^{2} 2 \mathrm{p}^{2}\); (d) \([\mathrm{Rn}] 7 \mathrm{~s}^{2} 6 \mathrm{~d}^{2}\) ?

Which elements are predicted to have the following groundstate electron configurations: (a) \([\mathrm{Ar}] 3 \mathrm{~d}^{10} 4 \mathrm{~s}^{2} 4 \mathrm{p}^{1}\); (b) \([\mathrm{Ne}] 3 \mathrm{~s}^{1}\); (c) \([\mathrm{Kr}] 5 \mathrm{~s}^{2}\); (d) \([\mathrm{Xe}] 4 \mathrm{f}^{7} 6 \mathrm{~s}^{2}\) ?

For each of the following ground-state atoms, predict the type of orbital (1s, \(2 \mathrm{p}, 3 \mathrm{~d}, 4 \mathrm{f}\), etc.) from which an electron will be removed to form the \(+1\) ion: (a) Ge; (b) Mn; (c) Ba; (d) Au.

For each of the following ground-state atoms, predict the type of orbital (1s, \(2 \mathrm{p}, 3 \mathrm{~d}, 4 \mathrm{f}\), etc.) from which an electron will be removed to form the \(+1\) ion: (a) \(\mathrm{Zn}\); (b) \(\mathrm{Cl}\); (c) \(\mathrm{Al}\); (d) \(\mathrm{Cu}\).

Predict the number of valence electrons present in each of the following atoms (include the outermost d-electrons: (a) \(\mathrm{N}\); (b) Ag; (c) \(\mathrm{Nb}\); (d) W.

Predict the number of valence electrons present in each of the following atoms (include the outermost d-electrons): (a) Bi; (b) Ba; (c) \(\mathrm{Mn}\); (d) Zn.

How many unpaired electrons are predicted for the groundstate configuration of each of the following atoms: (a) Bi; (b) Si; (c) Ta; (d) Ni?

How many unpaired electrons are predicted for the groundstate configuration of each of the following atoms: (a) \(\mathrm{Pb}\); (b) Ir; (c) Y; (d) Cd?

The elements Ga, Ge, As, Se, and Br lie in the same period in the periodic table. Write the electron configuration expected for the ground-state atoms of these elements and predict how many unpaired electrons, if any, each atom has.

The elements \(\mathrm{N}, \mathrm{P}, \mathrm{As}, \mathrm{Sb}\), and Bi belong to the same group in the periodic table. Write the electron configuration expected for the ground-state atoms of these elements and predict how many unpaired electrons, if any, each atom has.

Give the notation for the valence-shell configuration (including the outermost d-electrons) of (a) the alkali metals; (b) Group 15/V elements; (c) Group 5 transition metals; (d) "coinage" metals (Cu, Ag, Au).

Give the notation for the valence-shell configuration (including the outermost d-electrons) of (a) the halogens; (b) the chalcogens (the Group 16/VI elements); (c) the transition metals in Group \(5 ;\) (d) the Group 14/IV elements.

Arrange the elements in each of the following sets in order of decreasing atomic radius: (a) sulfur, chlorine, silicon; (b) cobalt, titanium, chromium; (c) zinc, mercury, cadmium; (d) antimony, bismuth, phosphorus.