### Short Answer

### 21.1 Planck and Quantum Nature of Light

- The curve would appear as a Gaussian probability distribution with a large peak in the middle.
- The curve would appear as a vertical line.
- The curve would appear as a horizontal line.
- The curve would appear as a diagonal line correlating intensity to frequency at a 1:1 ratio.

Because there are more gradations to high frequency radiation than low frequency radiation, scientists also thought it possible that a curve titled the *ultraviolet catastrophe* would occur. Explain what the blackbody radiation curve would look like if this were the case.

- The curve would steadily increase in intensity with increasing frequency.
- The curve would steadily decrease in intensity with increasing frequency.
- The curve would be much steeper than in the blackbody radiation graph.
- The curve would be much flatter than in the blackbody radiation graph.

Energy provided by a light exists in the following quantities: 150 J, 225 J, 300 J. Define one possible quantum of energy and provide an energy state that cannot exist with this quantum.

- 65 J; 450 J cannot exist
- 70 J; 450 J cannot exist
- 75 J; 375 J cannot exist
- 75 J; 100 J cannot exist

- Planckâ€™s constant is smaller than any previous discovered constant.
- Planck hypothesized that energy is quantized rather than continuous.
- Planckâ€™s theories meant that classical physics was no longer useful for any system.
- Plank discovered the blackbody radiation spectrum.

How many 500-mm microwave photons are needed to supply the 8 kJ of energy necessary to heat a cup of water by 10 degrees Celsius?

- 8.05 Ã— 10
^{28}photons - 8.05 Ã— 10
^{26}photons - 2.01 Ã— 10
^{26}photons - 2.01 Ã— 10
^{28}photons

What is the efficiency of a 100-W, 550-nm lightbulb if a photometer finds that 1 Ã— 10^{20} photons are emitted each second?

- 101 percent
- 72 percent
- 18 percent
- 36 percent

- Gamma rays
- Radio waves
- Ultraviolet light
- X-rays

- Photons of gamma rays and X-rays carry with them less energy.
- Photons of gamma rays and X-rays have longer wavelengths.
- Photons of gamma rays and X-rays have lower frequencies.
- Photons of gamma rays and X-rays carry with them more energy.

### 21.2 Einstein and the Photoelectric Effect

According to wave theory, what is necessary to eject electrons from a surface?

- Enough energy to overcome the binding energy of the electrons at the surface
- A frequency that is higher than that of the electrons at the surface
- Energy that is lower than the binding energy of the electrons at the surface
- A very small number of photons

What is the wavelength of EM radiation that ejects 2.00-eV electrons from calcium metal, given that the binding energy is 2.71 eV?

- 16.1 Ã— 10
^{5}m - 6.21 Ã— 10
^{âˆ’5}m - 9.94 Ã— 10
^{âˆ’26}m - 2.63 Ã— 10
^{-7}m

- $6.22\xc3\u2014{10}^{\xe2\u02c6\u20197}\phantom{\rule{thinmathspace}{0ex}}\text{m}$
- $5.92\xc3\u2014{10}^{\xe2\u02c6\u20195}\phantom{\rule{thinmathspace}{0ex}}\text{m}$
- $1.24\xc3\u2014{10}^{\xe2\u02c6\u20195}\phantom{\rule{thinmathspace}{0ex}}\text{m}$
- $5.31\xc3\u2014{10}^{\xe2\u02c6\u20197}\phantom{\rule{thinmathspace}{0ex}}\text{m}$

- The lightâ€™s wavelength was about 837 nm.
- The lightâ€™s wavelength was about 886 nm.
- The lightâ€™s wavelength was about 908 nm.
- The lightâ€™s wavelength was about 950 nm.

- Solar panels take advantage of the photoelectric effect to store potential energy as heat.
- Solar panels take advantage of the photoelectric effect to convert heat energy into power.
- Solar panels take advantage of the photoelectric effect to generate power from incoming radiation.
- Solar panels take advantage of the photoelectric effect to create light from incoming heat energy.

### 21.3 The Dual Nature of Light

- The photonâ€™s wavelength will drop to zero.
- The photonâ€™s wavelength will decrease.
- The photonâ€™s wavelength will increase.
- The photonâ€™s wavelength will be inverted.

- Their momentums are the same because they have the same energy.
- The electron has a greater momentum than the photon; photon momentum arises from Planckâ€™s constant which is many orders of magnitude smaller than the mass of an electron.
- The photon has a greater momentum than the electron; photon momentum arises from the speed of light which is much faster than an electron can move.
- The photon must have a momentum of zero because its rest mass is zero.

A 500-nm photon strikes an electron and loses 20 percent of its energy. What is the new momentum of the photon?

- 4.24 Ã— 10
^{âˆ’27}kg â‹… m/s - 3.18 Ã— 10
^{âˆ’27}kg â‹… m/s - 2.12 Ã— 10
^{âˆ’27}kg â‹… m/s - 1.06 Ã— 10
^{âˆ’27}kg â‹… m/s

A 500-nm photon strikes an electron and loses 20 percent of its energy. What is the speed of the recoiling electron?

- 7.18 Ã— 10
^{5}m/s - 6.18 Ã— 10
^{5}m/s - 5.18 Ã— 10
^{5}m/s - 4.18 Ã— 10
^{5}m/s

When a photon strikes a solar sail, what is the direction of impulse on the photon?

- parallel to the sail
- perpendicular to the sail
- tangential to the sail
- opposite to the sail

- Solar sails rely on disorganized strikes from light particles, while sailboats rely on disorganized strikes from air particles.
- Solar sails rely on disorganized strikes from air particles, while sailboats rely on disorganized strikes from light particles.
- Solar sails rely on organized strikes from air particles, while sailboats rely on organized strikes from light particles.
- Solar sails rely on organized strikes from light particles, while sailboats rely on organized strikes from air particles.

The wavelength of a particle is called the de Broglie wavelength, and it can be found with the equation $p=\frac{h}{\mathrm{\xce\xbb}}$ .

Yes or noâ€”Can the wavelength of an electron match that of a proton?

- Yes, a slow-moving electron can achieve the same momentum as a slow-moving proton.
- No, a fast-moving electron cannot achieve the same momentum, and hence the same wavelength, as a proton.
- No, an electron can achieve the same momentum, and hence not the same wavelength, as a proton.
- Yes, a fast-moving electron can achieve the same momentum, and hence have the same wavelength, as a slow-moving proton.

- The length of the wave is the same as the diameter of the ball, so they are indistinguishable.
- The length of the wave is longer than the diameter of the ball, making the wave difficult to observe.
- The length of the wave is much shorter than the diameter of the ball, making the wave difficult to observe.
- The ball is not rolling quickly enough to have wave-like qualities.