Test Prep for AP® Courses

The visible spectrum of sunlight shows a range of colors from red to violet. This spectrum has numerous dark lines spread throughout it. Noting that the surface of the Sun is much cooler than the interior, so that the surface is comparable to a cool gas through which light passes, which of the following statements correctly explains the dark lines?

1. The cooler, denser surface material scatters certain wavelengths of light, forming dark lines.
2. The atoms at the surface absorb certain wavelengths of light, causing the dark lines at those wavelengths.
3. The atoms in the Sun’s interior emit light of specific wavelength, so that parts of the spectrum are dark.
4. The atoms at the surface are excited by the high interior temperatures, so that the dark lines are merely wavelengths at which those atoms don’t emit energy.

A metal exposed to a beam of light with a wavelength equal to or shorter than a specific wavelength emits electrons. What property of light, as described in the quantum explanation of blackbody radiation, accounts for this photoelectric process?

1. The energy of light increases as its speed increases.
2. The energy of light increases as its intensity increases.
3. The energy of light increases as its frequency increases.
4. The energy of light increases as its wavelength increases.

A microwave oven produces electromagnetic radiation in the radio portion of the spectrum. These microwave photons are absorbed by water molecules, resulting in an increase in the molecules’ rotational energies. This added energy is transferred by heat to the surrounding food, which as a result becomes hot very quickly. If the energy absorbed by a water molecule is 1.0 × 10^–5 eV, what is the corresponding wavelength of the microwave photons?

1. 1.22 GHz
2. 2.45 GHz
3. 4.90 GHz
4. 9.80 Hz

The mass of a proton is 1.67 × 10^–27 kg. If a proton has the same momentum as a photon with a wavelength of 325 nm, what is its speed?

1. 2.73 × 10^–3 m/s
2. 0.819 m/s
3. 1.22 m/s
4. 2.71 × 10⁴ m/s

In an experiment in which the Compton effect is observed, a “gamma ray” photon with a wavelength of 5.00 × 10^–13 m scatters from an electron. If the change in the electron energy is 1.60 × 10^–15 J, what is the wavelength of the photon after the collision with the electron?

1. 4.95 × 10^–13 m
2. 4.98 × 10^–13 m
3. 5.02 × 10^–13 m
4. 5.05 × 10^–13 m

The ground state of a certain type of atom has energy of –E₀. What is the wavelength of a photon with enough energy to ionize the atom when it is in the ground state, so that the ejected electron has kinetic energy equal to 2E₀?

1. $\lambda =\frac{hc}{3E_0}$
2. $\lambda =\frac{hc}{2E_0}$
3. $\lambda =\frac{hc}{E_0}$
4. $\lambda =\frac{2hc}{E_0}$

The least massive particle known to exist is the electron neutrino. Though scientists once believed that it had no mass, like the photon, they have now determined that this particle has an extremely low mass, equivalent to a few electron volts. Assuming a mass of 2.2 eV/c² (or 3.9 × 10^–36 kg) and a speed of 4.4 × 10⁶ m/s, which of the following values equals the neutrino’s de Broglie wavelength?

1. 3.8 × 10^–5 m
2. 4.7 × 10^–7 m
3. 1.7 × 10^–10 m
4. 8.9 × 10^–14 m

In a Davisson-Germer type of experiment, a crystal with a parallel-plane separation (d) of 9.1 × 10^–2 nm produces constructive interference with an electron beam at an angle of θ = 50°. Which of the following is the maximum de Broglie wavelength for these electrons?

1. 0.07nm
2. 0.09 nm
3. 0.14 nm
4. 0.21 nm

Which of the following describes one of the main features of wave-particle duality?

1. As speed increases, the wave nature of matter becomes more evident.
2. As momentum decreases, the particle nature of matter becomes more evident.
3. As energy increases, the wave nature of matter becomes easier to observe.
4. As mass increases, the wave nature of matter is less easy to observe.