Q: A blackbody emits radiation with a peak wavelength of 500 nm. Using Wien’s Law, what is the approximate surface temperature of the blackbody?

$$T = \frac{2.90 \times 10$$^{-3}$$ \text{ m K}}{500 \times 10$$^{-9}$$ \text{ m}} = 5800 \text{ K}$$

Q: A material has a work function of $$4.55 eV. $$What is the threshold wavelength $$\lambda_c$$ for the photoelectric effect in this material?

$$\lambda_c = \frac{hc}{\phi} = \frac{(6.63 \times 10$$^{-34}$$ \text{ J s})(3.00 \times 10^8$ \text{ m/s})}{4.55 \times 1.60 \times 10$$^{-19}$$ \text{ J}} \approx 273 \text{ nm}$$

Q: An electron is moving at $$6 \times 10^6$ m/s. What is its de Broglie wavelength?

$$\lambda = \frac{6.63 \times 10$$^{-34}$$ \text{ J s}}{(9.11 \times 10$$^{-31}$$ \text{ kg})(6 \times 10^6$ \text{ m/s})} \approx 1.21 \times 10$$^{-10}$$ \text{ m}$$

Question 1

Which law describes the total power radiated by a blackbody as a function of its temperature and surface area?

Accepted Answer

Stefan-Boltzmann Law: $$P = \sigma A T^4$

Question 2

A blackbody emits radiation with a peak wavelength of 500 nm. Using Wien’s Law, what is the approximate surface temperature of the blackbody?

Accepted Answer

$$T = \frac{2.90 	imes 10$$^{-3}$$ 	ext{ m K}}{500 	imes 10$$^{-9}$$ 	ext{ m}} = 5800 	ext{ K}$$

Question 3

Which of the following statements about blackbody radiation is correct?

Accepted Answer

All blackbodies at the same temperature emit exactly the same spectrum.

Question 4

According to Planck’s Law, which constant was introduced to fit the experimental data of blackbody radiation?

Accepted Answer

Planck constant ($$h)$$

Question 5

Einstein’s explanation of the photoelectric effect led to the concept of photons. What is the energy of a photon with frequency $$f$$?

Accepted Answer

$$E = hf$$

Question 6

In the photoelectric effect, what happens if the frequency of incident light is below the threshold frequency $$f_c$$ for a given metal?

Accepted Answer

No electrons are emitted from the metal surface.

Question 7

A photon with energy less than the work function $$\phi of a $$metal strikes the surface. What is the outcome?

Accepted Answer

No electrons are emitted.

Question 8

Which experimental result from the photoelectric effect could NOT be explained by classical theories?

Accepted Answer

Electrons are ejected immediately once light hits the metal surface.

Question 9

The stopping potential $$\Delta V_{stop} in a $$photoelectric experiment is related to the maximum kinetic energy of the ejected electrons. Which equation expresses this relationship?

Accepted Answer

$$K_{max} = e \Delta V_{stop}$$

Question 10

A material has a work function of $$4.55 eV. $$What is the threshold wavelength $$\lambda_c$$ for the photoelectric effect in this material?

Accepted Answer

$$\lambda_c = \frac{hc}{\phi} = \frac{(6.63 	imes 10$$^{-34}$$ 	ext{ J s})(3.00 	imes 10^8$ 	ext{ m/s})}{4.55 	imes 1.60 	imes 10$$^{-19}$$ 	ext{ J}} \approx 273 	ext{ nm}$$

Question 11

Which of the following best describes the wave-particle duality of light?

Accepted Answer

Light can behave as either a wave or a particle depending on the experiment.

Question 12

According to de Broglie, what is the wavelength associated with a particle of mass $$m$$ moving at velocity $$v$$?

Accepted Answer

$$\lambda = \frac{h}{mv}$$

Question 13

An electron is moving at $$6 	imes 10^6$ m/s. What is its de Broglie wavelength?

Accepted Answer

$$\lambda = \frac{6.63 	imes 10$$^{-34}$$ 	ext{ J s}}{(9.11 	imes 10$$^{-31}$$ 	ext{ kg})(6 	imes 10^6$ 	ext{ m/s})} \approx 1.21 	imes 10$$^{-10}$$ 	ext{ m}$$

Question 14

In the double-slit experiment with electrons, what is observed when electrons are fired one at a time?

Accepted Answer

An interference pattern builds up over time.

Question 15

Which equation describes the condition for constructive interference in a double-slit experiment?

Accepted Answer

$$d \sin 	heta = m \lambda$$

Question 16

A photon has a wavelength of $$4.00 	imes 10$$^{-7}$$ m. What is its momentum?

Accepted Answer

$$p = \frac{h}{\lambda} = \frac{6.63 	imes 10$$^{-34}$$ 	ext{ J s}}{4.00 	imes 10$$^{-7}$$ 	ext{ m}} = 1.66 	imes 10$$^{-27}$$ 	ext{ kg m/s}$$

Question 17

Which of the following is a consequence of the photoelectric effect experiment?

Accepted Answer

The energy of photoelectrons depends on the frequency of light.

Question 18

A microwave oven operates at 2.4 GHz. What is the energy of each microwave photon?

Accepted Answer

$$E = hf = (6.63 	imes 10$$^{-34}$$ 	ext{ J s})(2.4 	imes 10^9$ 	ext{ Hz}) = 1.59 	imes 10$$^{-24}$$ 	ext{ J}$$

Question 19

Which part of the electromagnetic spectrum does the cosmic background radiation at $$T = 2.728 K $$peak, according to Wien’s Law?

Accepted Answer

Microwave region

Quantum Physics: Blackbody Radiation, Photoelectric Effect, and Wave-Particle Duality

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