Chapter 5

Describe how the frequency of electromagnetic radiation is related to its wavelength.

Light is given off by a sodium- or mercury-containing streetlight when the atoms are excited in some way. The light you see arises for which of these reasons? (a) Electrons moving from a given quantum level to one of higher \(n\). (b) Electrons being removed from the atom, thereby creating a metal cation. (c) Electrons moving from a given quantum level to one of lower \(n\). (d) Electrons whizzing about the nucleus in an absolute frenzy.

What is Hund's rule? Give an example of its use.

Explain what it means when someone says, "An electron occupies the \(3 p_{x}\) orbital"

Describe the changes in atomic size and ionization energy across a period and down a group.

Why is the radius of \(\mathrm{Na}^{+}\) much smaller than the radius of Na? Why is the radius of \(\mathrm{Cl}^{-}\) much larger than the radius of \(\mathrm{Cl} ?\)

Write electron configurations to show the first two ionization steps for potassium. Explain why the second ionization energy is much larger than the first.

Explain how and why the sizes of atoms change across a period of the periodic table.

Write the electron configurations for the valence electrons of elements in the first three periods in Groups \(1 \mathrm{~A}\) through 8 A.

NASA operates a jetliner fitted with a special telescope that looks into outer space. The telescope has a camera that detects wavelengths between 5 and \(40 \mu \mathrm{m}\). During eight-hour flights at \(12,000 \mathrm{~m}\) above Earth, the plane will gather data of the nearby universe. (a) In what region of the electromagnetic spectrum does the camera operate? (b) Calculate the range of frequencies the camera detects.

Many marine organisms exhibit bioluminescence, which occurs when excited molecules return to their lowest energy (ground) state by releasing photons in the visible (and other) region of the electromagnetic spectrum. The starfish, Plutonaster bifrons, bioluminesces at \(525 \mathrm{nm}\). (a) What color is the bioluminescence? (b) Calculate the frequency of this bioluminescence.

Many marine organisms exhibit bioluminescence, which occurs when excited singlet-state molecules return to their lowest energy (ground) state by releasing photons in the visible region (and beyond) of the electromagnetic spectrum. Photostomias guernei, a spiny-rayed oceanic fish, bioluminesces at \(470 . \mathrm{nm}\). (a) What color is the bioluminescence? (b) Calculate the frequency of this bioluminescence.

Calculate the energy of a photon of blue light that has a wavelength of \(450 \mathrm{nm}\)

Calculate the wavelength and energy per photon associated with one quantum of laser light that has a frequency of \(4.57 \times 10^{14} \mathrm{~s}^{-1}\)

Stratospheric ozone absorbs damaging UV-C radiation from the sun, preventing the radiation from reaching Earth's surface. Calculate the frequency and energy per photon of UV-C radiation that has a wavelength of \(270 . \mathrm{nm}\)

When someone uses a sunscreen, which kind of radiation is blocked? How does the sunscreen protect your skin from this type of radiation?

Describe the role Einstein's explanation of the photoelectric effect played in the development of the quantum theory.

Light of very long wavelength strikes a photosensitive metallic surface and no electrons are ejected. Explain why increasing the intensity of this light on the metal still will not cause the photoelectric effect.

A bright red light strikes a photosensitive surface and no electrons are ejected, even though dim blue light ejects electrons from the surface. Explain.

To eject electrons from the surface of potassium metal requires a minimum energy of \(3.68 \times 10^{-19} \mathrm{~J}\). When \(600 .-\mathrm{nm}\) photons shine on a potassium surface, will they cause the photoelectric effect? Explain.

To eject electrons from a gold surface requires photons with a frequency equal to or greater than \(1.29 \times 10^{15} \mathrm{~Hz}\). Will photons in the visible region of the spectrum dislodge electrons from a gold surface? Explain.

A photoemissive material has a threshold energy, \(E_{\min }=\) \(5 \times 10^{-19} \mathrm{~J}\). Will \(300 . \mathrm{nm}\) radiation eject electrons from the material? Explain.

Flame tests depend on emissions in the visible region of the spectrum to identify elements in a sample. Bariumcontaining compounds emit at \(493 \mathrm{nm}\); strontiumcontaining compounds emit at \(642 \mathrm{nm}\). (a) Determine the identifying color of the flame test in each case. (b) Calculate the energy (J/photon) associated with each of these emissions. (c) Explain why the barium emission occurs at lower wavelength than the strontium does.

In Problem-Solving Example \(5.4,\) the wavelength of an \(n=2\) to \(n=5\) transition in a hydrogen atom was calculated to be \(434.1 \mathrm{nm} .\) In Table \(4.2,\) the standard formation enthalpy for liquid water is given as \(-285.830 \mathrm{~kJ} / \mathrm{mol}\). Use this information to calculate which process involves more energy per gram of hydrogen - the electronic transition from \(n=2\) to \(n=5\) in a hydrogen atom or the combustion of hydrogen and oxygen gas to produce liquid water.

Energy is emitted from an atom when an electron moves from a(n) _________ state to the ________ . The energy of the emitted radiation corresponds to the __________ between the two energy levels.

For which of these transitions in a hydrogen atom is energy absorbed? Emitted? (a) \(n=1\) to \(n=3\) (b) \(n=5\) to \(n=1\) (c) \(n=2\) to \(n=4\) (d) \(n=5\) to \(n=4\)

Calculate the energy and wavelength of the photon associated with the electron transition from \(n=2\) to \(n=5\) in the hydrogen atom.

Calculate the energy and the wavelength of the photon associated with an electron transition from \(n=1\) to \(n=4\) in the hydrogen atom.

Spectroscopists have observed \(\mathrm{He}^{+}\) in outer space. This ion is a one-electron species like a neutral hydrogen atom. Calculate the energy of the photon emitted for the transition from the \(n=5\) to the \(n=3\) state in this ion using the equation: \(E_{n}=-Z^{2} / n^{2}\left(2.179 \times 10^{-18} \mathrm{~J}\right) . \mathrm{Z}\) is the positive charge of the nucleus and \(n\) is the principal quantum number. In what part of the electromagnetic spectrum does this radiation lie?

The Bohr equation for hydrogen can be modified to apply to one-electron species other than uncharged hydrogen atoms, for example \(\mathrm{Li}^{2+},\) to calculate the energy of electron transitions in the ion. The modified equation is \(E_{n}=-Z^{2} / n^{2}\left(2.179 \times 10^{-18} \mathrm{~J}\right) . Z\) is the pos- itive charge of the nucleus and \(n\) is the principal quantum number. Calculate the energy of the photon emitted for the transition from the \(n=4\) to the \(n=1\) state in this ion. In what region of the electromagnetic spectrum does it lie?

The Brackett series of emissions has \(n_{\mathrm{f}}=4\). (a) Calculate the wavelength, in nanometers, of the photon emitted by the \(n=7\) to \(n=4\) transition. (b) In what region of the electromagnetic spectrum is the emitted radiation?

Arrange these items from smallest to largest de Broglie wavelength: baseball; bowling ball; electron moving at the velocity of light; the Moon; neon atom.

Arrange these items from largest to smallest de Broglie wavelength: basketball; proton; potassium atom; the planet Venus; soccer ball.

Compare and contrast the representations of electron density in an atom provided by dot-density diagrams and boundary-surface diagrams.

Assign a correct set of four quantum numbers for (a) Each electron in a boron atom. (b) The \(3 s\) electrons in a magnesium atom. (c) A \(3 d\) electron in an iron atom.

Assign a correct set of four quantum numbers for (a) Each electron in a nitrogen atom. (b) The valence electron in a sodium atom. (c) A \(3 d\) electron in a nickel atom.

Some of these sets of quantum numbers \(\left(n, \ell, m_{\ell}, m_{s}\right)\) could not occur. Explain why. $$ \text { (a) } 2,1,2,+\frac{1}{2} $$ (b) \(3,2,0,-\frac{1}{2}\) (c) 1,0,0,1 (d) \(3,3,2,-\frac{1}{2}\) $$ \text { (e) } 2,0,0,+\frac{1}{2} $$

One electron has the set of quantum numbers \(n=3\), \(\ell=1, m_{\ell}=-1,\) and \(m_{s}=+\frac{1}{2} ;\) another electron has the $$ \text { set } n=3, \ell=1, m_{\ell}=1, \text { and } m_{s}=+\frac{1}{2} \text { . } $$ (a) Could the electrons be in the same atom? Explain. (b) Could they be in the same atomic orbital? Explain.

Give the \(n, \ell,\) and \(m_{\ell}\) values for (a) Each atomic orbital in the \(6 f\) sublevel. (b) Each atomic orbital in the \(n=5\) level.

How many elements are there in the fourth period of the periodic table? Based on quantum theory, explain why it is not possible for there to be another element in this period.

From memory, sketch the shape of the boundary surface for each of these atomic orbitals: (a) \(4 d_{x^{2}-y^{2}}\) (b) \(2 s\) (c) \(3 p_{y}\)

From memory, sketch the shape of the boundary surface for each of these atomic orbitals: (a) \(2 p_{z}\) (b) \(4 s\) (c) \(3 d_{x y}\)

How many subshells are there in the electron shell with the principal quantum number \(n=4 ?\)

How many subshells are there in the electron shell with the principal quantum number \(n=5 ?\)

Titanium metal and \(\mathrm{Cr}^{2+}\) have the same number of electrons. However, the electron configuration of Ti is \([\mathrm{Ar}] 4 s^{2} 3 d^{2},\) but that of \(\mathrm{Cr}^{2+}\) is \([\mathrm{Ar}] 3 d^{4} .\) Explain.

Consider a \(2+\) ion that has six \(3 d\) electrons; which ion is it? Which \(2+\) ion would have only three \(3 d\) electrons?

Germanium had not been discovered in the 1870 s when Mendeleev formulated his ideas of chemical periodicity. He predicted its existence, however, and germanium was found in 1886 by Winkler. Write the electron configuration of germanium.

Write electron configurations for these atoms. (a) Strontium (Sr), named for a town in Scotland. (b) Tin (Sn), a metal used in the ancient world. Alloys of tin (solder, bronze, and pewter) are important.

Name an element of Group 6 A. What does the group designation tell you about the electron configuration of the element?

Name an element of Group 3A. What does the group designation tell you about the electron configuration of the element?