Chapter 2

What does it mean for something to have wavelike properties? Particulate properties? Electromagnetic radiation can be discussed in terms of both particles and waves. Explain the experimental verification for each of these views.

Defend and criticize Bohr's model. Why was it reasonable that such a model was proposed, and what evidence was there that it "works"? Why do we no longer "believe" in it?

Compare the first ionization energy of helium to its second ionization energy, remembering that both electrons come from the \(1 s\) orbital. Explain the difference without using actual numbers from the text.

Which has the larger second ionization energy, lithium or beryllium? Why?

Explain why a graph of ionization energy versus atomic num ber (across a row) is not linear. Where are the exceptions? Why are there exceptions?

Account for the fact that the line that separates the metals from the nonmetals on the periodic table is diagonal downward to the right instead of horizontal or vertical.

Explain electron from a quantum mechanical perspective, including a discussion of atomic radii, probabilities, and orbitals.

Choose the best response for the following. The ionization energy for the chlorine atom is equal in magnitude to the electron affinity for a. the Cl atom. b. the \(\mathrm{Cl}^{-}\) ion. c. the \(\mathrm{Cl}^{+}\) ion. d. the \(F\) atom. e. none of these.

Consider the following statement: "The ionization energy for the potassium atom is negative, because when K loses an electron to become \(\mathbf{K}^{+}\), it achieves a noble gas electron configuration" Indicate everything that is correct in this statement. Indicate everything that is incorrect. Correct the incorrect information and explain.

In going across a row of the periodic table, electrons are added and ionization energy generally increases. In going down a column of the periodic table, electrons are also being added but ionization energy decreases. Explain.

What is meant by an orbital?

Explain the difference between the probability density distribution for an orbital and its radial probability.

Is the following statement true or false? The hydrogen atom has a \(3 s\) orbital. Explain.

Which is higher in energy, the \(2 s\) or \(2 p\) orbital, in hydrogen? Is this also true for helium? Explain.

Prove mathematically that it is more energetically favorable for a fluorine atom to take an electron from a sodium atom than for a fluorine atom to take an electron from another fluorine atom.

What type of relationship (direct or inverse) exists between wavelength, frequency, and photon energy? What does a photon energy unit of a joule equal?

What do we mean by the frequency of electromagnetic radiation? Is the frequency the same as the speed of the electromagnetic radiation?

Explain the photoelectric effect.

Describe briefly why the study of electromagnetic radiation has been important to our understanding of the arrangement of electrons in atoms.

The Bohr model works for only one electron species. Why do we discuss it in this text (what's good about it)?

Many times the claim is made that subshells half-filled with electrons are particularly stable. Can you suggest a possible physical basis for this claim?

Diagonal relationships in the periodic table exist as well as the vertical relationships. For example, Be and Al are similar in some of their properties, as are \(\mathrm{B}\) and \(\mathrm{Si}\). Rationalize why these diagonal relationships hold for properties such as size, ionization energy, and electron affinity.

Elements with very large ionization energies also tend to have highly negative (favorable) electron affinities. Explain. Which group of elements would you expect to be an exception to this statement?

The changes in electron affinity as one goes down a group in the periodic table are not nearly as large as the variations in ionization energies. Why?

Why is it much harder to explain the line spectra of polyelectronic atoms and ions than it is to explain the line spectra of hydrogen and hydrogenlike ions?

Scientists use emission spectra to confirm the presence of an element in materials of unknown composition. Why is this possible?

Does the minimization of electron-electron repulsions correlate with Hund's rule?

In the hydrogen atom, what is the physical significance of the state for which \(n=\infty\) and \(E=0 ?\)

The work function is the energy required to remove an electron from an atom on the surface of a metal. How does this definition differ from that for ionization energy?

Many more anhydrous lithium salts are hygroscopic (readily absorb water) than are those of the other alkali metals. Explain.

The laser in an audio CD player uses light with a wavelength of \(7.80 \times 10^{2} \mathrm{nm} .\) Calculate the frequency of this light.

An FM radio station broadcasts at 99.5 MHz. Calculate the wavelength of the corresponding radio waves.

Microwave radiation has a wavelength on the order of \(1.0 \mathrm{cm} .\) Calculate the frequency and the energy of a single photon of this radiation.

A photon of ultraviolet (UV) light possesses enough energy to mutate a strand of human DNA. What is the energy of a single UV photon and 1 mole of UV photons having a wavelength of \(25 \mathrm{nm} ? 1\) mol UV photons \(=6.022 \times 10^{23} \mathrm{UV}\) photons.

Octyl methoxycinnamate and oxybenzone are common ingredients in sunscreen applications. These compounds work by absorbing ultraviolet (UV) B light (wavelength \(280-320 \mathrm{nm}\) ), the UV light most associated with sunburn symptoms. What frequency range of light do these compounds absorb?

One type of electromagnetic radiation has a frequency of \(107.1 \mathrm{MHz},\) another type has a wavelength of \(2.12 \times 10^{-10} \mathrm{m}\) and another type of electromagnetic radiation has photons with energy equal to \(3.97 \times 10^{-19} \mathrm{J} /\) photon. Identify each type of electromagnetic radiation and place them in order of increasing photon energy and increasing frequency.

Carbon absorbs energy at a wavelength of \(150 . \mathrm{nm.}\) The total amount of energy emitted by a carbon sample is \(1.98 \times 10^{5} \mathrm{J}\) Calculate the number of carbon atoms present in the sample, assuming that each atom emits one photon.

X rays have wavelengths on the order of \(1 \times 10^{-10} \mathrm{m}\). Calculate the energy of \(1.0 \times 10^{-10} \mathrm{m}\) X rays in units of kilojoules per mole of X rays. (1 mol X rays \(=6.022 \times 10^{23}\) X rays.) AM radio waves have wavelengths on the order of \(1 \times 10^{4} \mathrm{m}\). Calculate the energy of \(1.0 \times 10^{4} \mathrm{m}\) radio waves in units of kilojoules per mole of radio waves. Consider that the bond energy of a carbon- carbon single bond found in organic compounds is 347 kJ/mol. Would X rays and/or radio waves be able to disrupt organic compounds by breaking carbon- carbon single bonds?

The work function of an element is the energy required to remove an electron from the surface of the solid element. The work function for lithium is \(279.7 \mathrm{kJ} / \mathrm{mol}\) (that is, it takes \(279.7 \mathrm{kJ}\) of energy to remove 1 mole of electrons from 1 mole of Li atoms on the surface of Li metal; 1 mol \(L i=6.022 \times\) \(10^{23}\) atoms Li). What is the maximum wavelength of light that can remove an electron from an atom on the surface of lithium metal?

It takes \(208.4 \mathrm{kJ}\) of energy to remove 1 mole of electrons from an atom on the surface of rubidium metal. (1 mol electrons = \(6.022 \times 10^{23}\) electrons. How much energy does it take to remove a single electron from an atom on the surface of solid rubidium? What is the maximum wavelength of light capable of doing this?

It takes \(7.21 \times 10^{-19} \mathrm{J}\) of energy to remove an electron from an iron atom. What is the maximum wavelength of light that can do this?

Ionization energy is the energy required to remove an electron from an atom in the gas phase. The ionization energy of gold is \(890.1 \mathrm{kJ} / \mathrm{mol} .\) Is light with a wavelength of \(225 \mathrm{nm}\) capable of ionizing a gold atom (removing an electron) in the gas phase? ( 1 mol gold \(=6.022 \times 10^{23}\) atoms gold.)

Calculate the de Broglie wavelength for each of the following. a. an electron with a velocity \(10 . \%\) of the speed of light b. a tennis ball \((55 \mathrm{g})\) served at \(35 \mathrm{m} / \mathrm{s}(\sim 80 \mathrm{mi} / \mathrm{h})\)

Neutron diffraction is used in determining the structures of molecules. a. Calculate the de Broglie wavelength of a neutron moving at \(1.00 \%\) of the speed of light. b. Calculate the velocity of a neutron with a wavelength of \(75 \mathrm{pm}\left(1 \mathrm{pm}=10^{-12} \mathrm{m}\right)\)

A particle has a velocity that is \(90 . \%\) of the speed of light. If the wavelength of the particle is \(1.5 \times 10^{-15} \mathrm{m},\) what is the mass of the particle?

Calculate the velocities of electrons with de Broglie wavelengths of \(1.0 \times 10^{2} \mathrm{nm}\) and \(1.0 \mathrm{nm} .\)

Calculate the wavelength of light emitted when each of the following transitions occur in the hydrogen atom. What type of electromagnetic radiation is emitted in each transition? a. \(n=3 \rightarrow n=2\) b. \(n=4 \rightarrow n=2\) c. \(n=2 \rightarrow n=1\)

Calculate the wavelength of light emitted when each of the following transitions occur in the hydrogen atom. What type of electromagnetic radiation is emitted in each transition? a. \(n=4 \rightarrow n=3\) b. \(n=5 \rightarrow n=4\) c. \(n=5 \rightarrow n=3\)

Calculate the longest and shortest wavelengths of light emitted by electrons in the hydrogen atom that begin in the \(n=6\) state and then fall to states with smaller values of \(n\).

Assume that a hydrogen atom's electron has been excited to the \(n=5\) level. How many different wavelengths of light can be emitted as this excited atom loses energy?