Chapter 7

What is a wave? Explain the following terms associated with waves: wavelength, frequency, amplitude.

What are the units for wavelength and frequency of electromagnetic waves? What is the speed of light in meters per second and miles per hour?

List the types of electromagnetic radiation, starting with the radiation having the longest wavelength and ending with the radiation having the shortest wavelength.

Give the high and low wavelength values that define the visible region of the electromagnetic spectrum.

Briefly explain Planck's quantum theory and explain what a quantum is. What are the units for Planck's constant?

Give two everyday examples that illustrate the concept of quantization.

(a) What is the frequency of light having a wavelength of \(456 \mathrm{nm} ?\) (b) What is the wavelength (in \(\mathrm{nm}\) ) of radiation having a frequency of \(2.45 \times 10^{9} \mathrm{~Hz}\) ? (This is the type of radiation used in microwave ovens.)

What are photons? What role did Einstein's explanation of the photoelectric effect play in the development of the particle-wave interpretation of the nature of electromagnetic radiation?

A photon has a wavelength of \(624 \mathrm{nm}\). Calculate the energy of the photon in joules.

The blue color of the sky results from the scattering of sunlight by air molecules. The blue light has a frequency of about \(7.5 \times 10^{14} \mathrm{~Hz}\). (a) Calculate the wavelength, in nanometers, associated with this radiation, and (b) calculate the energy, in joules, of a single photon associated with this frequency.

A photon has a frequency of \(6.0 \times 10^{4} \mathrm{~Hz}\). (a) Convert this frequency into wavelength (nm). Does this frequency fall in the visible region? (b) Calculate the energy (in joules) of this photon. (c) Calculate the energy (in joules) of 1 mole of photons all with this frequency.

What is the wavelength, in \(\mathrm{nm}\), of radiation that has an energy content of \(1.0 \times 10^{3} \mathrm{~kJ} / \mathrm{mol} ?\) In which region of the electromagnetic spectrum is this radiation found?

When copper is bombarded with high-energy electrons, X rays are emitted. Calculate the energy (in joules) associated with the photons if the wavelength of the X rays is \(0.154 \mathrm{nm}\).

A particular form of electromagnetic radiation has a frequency of \(8.11 \times 10^{14} \mathrm{~Hz}\). (a) What is its wavelength in nanometers? In meters? (b) To what region of the electromagnetic spectrum would you assign it? (c) What is the energy (in joules) of one quantum of this radiation?

The work function of potassium is \(3.68 \times 10^{-19} \mathrm{~J}\). (a) What is the minimum frequency of light needed to eject electrons from the metal? (b) Calculate the kinetic energy of the ejected electrons when light of frequency equal to \(8.62 \times 10^{14} \mathrm{~s}^{-1}\) is used for irradiation.

When light of frequency equal to \(2.11 \times 10^{15} \mathrm{~s}^{-1}\) shines on the surface of gold metal, the kinetic energy of ejected electrons is found to be \(5.83 \times 10^{-19} \mathrm{~J}\). What is the work function of gold?

(a) What is an energy level? Explain the difference between ground state and excited state. (b) What are emission spectra? How do line spectra differ from continuous spectra?

Explain why elements produce their own characteristic colors when they emit photons.

Some copper compounds emit green light when they are heated in a flame. How would you determine whether the light is of one wavelength or a mixture of two or more wavelengths?

Is it possible for a fluorescent material to emit radiation in the ultraviolet region after absorbing visible light? Explain your answer.

Explain how astronomers are able to tell which elements are present in distant stars by analyzing the electromagnetic radiation emitted by the stars.

Consider the following energy levels of a hypothetical atom: \(E_{4}\) \(-1.0 \times 10^{-19} \mathrm{~J}\) \(E_{3}\) \(--5.0 \times 10^{-19} \mathrm{~J}\) \(E_{2}\) \(--10 \times 10^{-19} \mathrm{~J}\) \(E_{1}\) \(-15 \times 10^{-19} \mathrm{~J}\) (a) What is the wavelength of the photon needed to excite an electron from \(E_{1}\) to \(E_{4} ?\) (b) What is the energy (in joules) a photon must have in order to excite an electron from \(E_{2}\) to \(E_{3} ?\) (c) When an electron drops from the \(E_{3}\) level to the \(E_{1}\) level, the atom is said to undergo emission. Calculate the wavelength of the photon emitted in this process.

Calculate the wavelength (in \(\mathrm{nm}\) ) of a photon emitted by a hydrogen atom when its electron drops from the \(n=5\) state to the \(n=3\) state.

Calculate the frequency (Hz) and wavelength (nm) of the emitted photon when an electron drops from the \(n=4\) to the \(n=2\) level in a hydrogen atom.

An electron in the hydrogen atom makes a transition from an energy state of principal quantum numbers \(n_{i}\) to the \(n=2\) state. If the photon emitted has a wavelength of \(434 \mathrm{nm}\), what is the value of \(n_{i} ?\)

Explain the statement, Matter and radiation have a "dual nature."

How does de Broglie's hypothesis account for the fact that the energies of the electron in a hydrogen atom are quantized?

(a) If a \(\mathrm{H}\) atom and a He atom are traveling at the same speed, what will be the relative wavelengths of the two atoms? (b) If a \(\mathrm{H}\) atom and a He atom have the same kinetic energy, what will be the relative wavelengths of the two atoms?

Thermal neutrons move at speeds comparable to those of air molecules at room temperature. These neutrons are most effective in initiating a nuclear chain reaction among \({ }^{235} \mathrm{U}\) isotopes. Calculate the wavelength (in \(\mathrm{nm}\) ) associated with a beam of neutrons moving at \(7.00 \times 10^{2} \mathrm{~m} / \mathrm{s}\). (Mass of a neutron \(\left.=1.675 \times 10^{-27} \mathrm{~kg} .\right)\)

Protons can be accelerated to speeds near that of light in particle accelerators. Estimate the wavelength (in \(\mathrm{nm}\) ) of such a proton moving at \(2.90 \times\) \(10^{8} \mathrm{~m} / \mathrm{s} .\) (Mass of a proton \(\left.=1.673 \times 10^{-27} \mathrm{~kg} .\right)\)

What is the de Broglie wavelength, in centimeters, of a 12.4-g hummingbird flying at \(1.20 \times 10^{2} \mathrm{mph} ?\) \((1 \mathrm{mile}=1.61 \mathrm{~km})\)

What is the de Broglie wavelength (in \(\mathrm{nm}\) ) associated with a 2.5 -g Ping-Pong ball traveling 35 mph?

What are the inadequacies of Bohr's theory?

What is the Heisenberg uncertainty principle? What is the Schrodinger equation?

What is the physical significance of the wave function?

How is the concept of electron density used to describe the position of an electron in the quantum mechanical treatment of an atom?

Describe the four quantum numbers used to characterize an electron in an atom.

Which quantum number defines a shell? Which quantum numbers define a subshell?

Which of the following orbitals do not exist: \(1 p, 2 s\) \(2 d, 3 p, 3 d, 3 f, 4 g ?\)

Which of the four quantum numbers \(\left(n, \ell, m_{\ell}, m_{s}\right)\) determine (a) the energy of an electron in a hydrogen atom and in a many- electron atom, (b) the size of an orbital, (c) the shape of an orbital, (d) the orientation of an orbital in space?

An electron in a certain atom is in the \(n=2\) quantum level. List the possible values of \(\ell\) and \(m_{t}\) that it can have.

An electron in an atom is in the \(n=3\) quantum level. List the possible values of \(\ell\) and \(m_{\ell}\) that it can have.

Give the values of the quantum numbers associated with the following orbitals: (a) \(2 p,\) (b) \(3 s,\) (c) \(5 d\).

Give the values of the four quantum numbers of an electron in the following orbitals: (a) \(3 s,\) (b) \(4 p\), (c) \(3 d\).

List all the possible subshells and orbitals associated with the principal quantum number \(n,\) if \(n=5\)

List all the possible subshells and orbitals associated with the principal guantum number \(n\), if \(n=6\).

What is an atomic orbital? How does an atomic orbital differ from an orbit?

Describe the shapes of \(s, p,\) and \(d\) orbitals. How are these orbitals related to the quantum numbers \(n, \ell\), and \(m_{\ell} ?\)

List the hydrogen orbitals in increasing order of energy.

Why is a boundary surface diagram useful in representing an atomic orbital?