### Short Answer

#### 21.1 Planck and Quantum Nature of Light

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

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

#### 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

#### 21.3 The Dual Nature of Light

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

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.