Chapter 8

Based on the relationship between electron configurations and the periodic table, give the number of (a) outer-shell electrons in an atom of \(\mathrm{Sb} ;\) (b) electrons in the fourth principal electronic shell of \(\mathrm{Pt} ;\) (c) elements whose atoms have six outer-shell electrons; (d) unpaired electrons in an atom of Te; (e) transition elements in the sixth period.

Use the basic rules for electron configurations to indicate the number of (a) unpaired electrons in an atom of \(\mathrm{P} ;\) (b) \(3 d\) electrons in an atom of \(\mathrm{Br} ;\) (c) \(4 p\) electrons in an atom of \(\mathrm{Ge} ;\) (d) \(6 \mathrm{s}\) electrons in an atom of \(\mathrm{Ba}\) (e) \(4 f\) electrons in an atom of Au.

Use orbital diagrams to show the distribution of electrons among the orbitals in (a) the \(4 p\) subshell of Br; (b) the \(3 d\) subshell of \(\mathrm{Co}^{2+},\) given that the two electrons lost are \(4 s ;\) (c) the \(5 d\) subshell of \(\mathrm{Pb}\).

The recently discovered element 114 should most closely resemble Pb. (a) Write the electron configuration of \(\mathrm{Pb}\). (b) Propose a plausible electron configuration for \(8 \equiv\) element 114.

Without referring to any tables or listings in the text, mark an appropriate location in the blank periodic table provided for each of the following: (a) the fifthperiod noble gas; (b) a sixth-period element whose atoms have three unpaired \(p\) electrons; (c) a \(d\) -block element having one \(4 \mathrm{s}\) electron; (d) a \(p\) -block element that is a metal.

What is the expected ground-state electron configuration for each of the following elements? (a) mercury; (b) calcium; (c) polonium; (d) tin; (e) tantalum; (f) iodine.

What is the expected ground-state electron configuration for each of the following elements? (a) tellurium; (b) cesium; (c) selenium; (d) platinum; (e) osmium; (f) chromium.

The following electron configurations correspond to the ground states of certain elements. Name each element. (a) \([\mathrm{Rn}] 7 s^{2} 6 d^{2} ;\) (b) \([\mathrm{He}] 2 s^{2} 2 p^{2} ;\) (c) \([\mathrm{Ar}] 3 d^{3} 4 s^{2}\) (d) \([\mathrm{Kr}] 4 d^{10} 5 s^{2} 5 p^{4} ;\) (e) \([\mathrm{Xe}] 4 f^{2} 6 s^{2} 6 p^{1}\)

The following electron configurations correspond to the ground states of certain elements. Name each element. (a) \([\mathrm{Ar}] 3 d^{10} 4 s^{2} 4 p^{3} ;\) (b) \([\mathrm{Ne}] 3 s^{2} 3 p^{4} ;\) (c) \([\mathrm{Ar}] 3 d^{1} 4 s^{2}\) (d) \([\mathrm{Kr}] 4 d^{6} 5 s^{2} ;\) (e) \([\mathrm{Xe}] 4 f^{12} 6 s^{2}\)

Electromagnetic radiation can be transmitted through a vacuum or empty space. Can heat be similarly transferred? Explain.

Infrared lamps are used in cafeterias to keep food warm. How many photons per second are produced by an infrared lamp that consumes energy at the rate of \(95 \mathrm{W}\) and is \(14 \%\) efficient in converting this energy to infrared radiation? Assume that the radiation has a wavelength of \(1525 \mathrm{nm}\).

In everyday usage, the term "quantum jump" describes a change of a very significant magnitude compared to more gradual, incremental changes; it is similar in meaning to the term "a sea change." Does quantum jump have the same meaning when applied to events at the atomic or molecular level? Explain.

The Pfund series of the hydrogen spectrum has as its longest wavelength component a line at \(7400 \mathrm{nm}\) Describe the electron transitions that produce this series. That is, give a Bohr quantum number that is common to this series.

Between which two orbits of the Bohr hydrogen atom must an electron fall to produce light of wavelength \(1876 \mathrm{nm} ?\)

Use appropriate relationships from the chapter to determine the wavelength of the line in the emission spectrum of \(\mathrm{He}^{+}\) produced by an electron transition from \(n=5\) to \(n=2\).

Draw an energy-level diagram that represents all the possible lines in the emission spectrum of hydrogen atoms produced by electron transitions, in one or more steps, from \(n=5\) to \(n=1\).

An atom in which just one of the outer-shell electrons is excited to a very high quantum level \(n\) is called a "high Rydberg" atom. In some ways, all these atoms resemble a Bohr hydrogen atom with its electron in a high-numbered orbit. Explain why you might expect this to be the case.

Radio signals from Voyager 1 in the 1970 s were broadcast at a frequency of 8.4 GHz. On Earth, this radiation was received by an antenna able to detect signals as weak as \(4 \times 10^{-21} \mathrm{W}\). How many photons per second does this detection limit represent?

The angular momentum of an electron in the Bohr hydrogen atom is mur , where \(m\) is the mass of the electron, \(u,\) its velocity, and \(r,\) the radius of the Bohr orbit. The angular momentum can have only the values nh/2 \(\pi\), where \(n\) is an integer (the number of the Bohr orbit). Show that the circum frences of the various Bohr orbits are integral multiples of the de Broglie wavelengths of the electron treated as a matter wave.

A molecule of chlorine can be dissociated into atoms by absorbing a photon of sufficiently high energy. Any excess energy is translated into kinetic energy as the atoms recoil from one another. If a molecule of chlorine at rest absorbs a photon of 300 nm wavelength, what will be the velocity of the two recoiling atoms? Assume that the excess energy is equally divided between the two atoms. The bond energy of \(\mathrm{Cl}_{2}\) is \(242.6 \mathrm{kJ} \mathrm{mol}^{-1}\)

Show that the volume of a spherical shell of radius \(r\) and thickness \(d r\) is \(4 \pi r^{2} d r .\) [Hint: This exercise requires calculus.]

In the ground state of a hydrogen atom, what is the probability of finding an electron anywhere in a sphere of radius (a) \(a_{0},\) or \(\left(\text { b) } 2 a_{0} ?\right.\)

When atoms in excited states collide with unexcited atoms they can transfer their excitation energy to those atoms. The most efficient energy transfer occurs when the excitation energy matches the energy of an excited state in the unexcited atom. Assuming that we have a collection of excited hydrogen atoms in the \(2 s^{1}\) excited state, are there any transitions of \(\mathrm{He}^{+}\) that could be most efficiently excited by the hydrogen atoms?

In your own words, define the following terms or symbols: (a) \(\lambda ;\) (b) \(\nu ;\) (c) \(h ;\) (d) \(\psi ;\) (e) principal quantum number, \(n\).

Briefly describe each of the following ideas or phenomena: (a) atomic (line) spectrum; (b) photoelectric effect; (c) matter wave; (d) Heisenberg uncertainty principle; (e) electron spin; (f) Pauli exclusion principle; (g) Hund's rule; (h) orbital diagram; (i) electron charge density; (j) radial electron density.

Explain the important distinctions between each pair of terms: (a) frequency and wavelength; (b) ultraviolet and infrared light; (c) continuous and discontinuous spectra; (d) traveling and standing waves; (e) quantum number and orbital; (f) spd f notation and orbital diagram; (g) \(s\) block and \(p\) block; (h) main group and transition element; (i) the ground state and excited state of a hydrogen atom.

Describe two ways in which the orbitals of multielectron atoms resemble hydrogen orbitals and two ways in which they differ from hydrogen orbitals.

Explain the phrase \(e\)ffective nuclear charge. How is this related to the shielding effect?

If traveling at equal speeds, which of the following matter waves has the longest wavelength? Explain. (a) electron; (b) proton; (c) neutron; (d) \(\alpha\) particle \(\left(\mathrm{He}^{2+}\right)\).

For electromagnetic radiation transmitted through a vacuum, state whether each of the following properties is directly proportional to, inversely proportional to, or independent of the frequency: (a) velocity; (b) wavelength; (c) energy per mole. Explain.

Construct a concept map representing the ideas of modern quantum mechanics.

Construct a concept map for the configurations of multielectron atoms.