Q: A metal has a work function $$E_0 = 4.28$$\ \text{eV}$$. What is the minimum frequency of light required to eject electrons from this metal? (Planck's constant h = 4.14$$ \times $$10^{-15}$$\ \text{eV} \cdot \text{s}$$)

$$f_0 = 1.03$$ \times $$10^{15}$$\ \text{Hz}$$

Q: A red laser pointer emits light at $$\lambda = 650\ \text{nm}$$ with a power of $$2.0\ \text{mW}. $$How many photons does it emit per second? (Use $$h = 6.63 \times 10$$^{-34}$$\ \text{J} \cdot \text{s}$$, $$c = 3.00 \times 10^8$\ \text{m/s})$$

$$6.5 \times 10$$^{15}$$ photons/s

Q: What is the de Broglie wavelength of an electron (mass $$9.11 \times 10$$^{-31}$$\ \text{kg}) $$moving at $$2.0 \times 10^6$\ \text{m/s}$$? (Planck's constant $$h = 6.63 \times 10$$^{-34}$$\ \text{J} \cdot \text{s})$$

$$3.6 \times 10$$^{-10}$$\ \text{m}$$

Q: In the Bohr model of the hydrogen atom, what is the energy of the electron in the $$nth $$stationary state?

$$E_n = -\dfrac{13.60\ \text{eV}}{n^2$}$$

Q: Which of the following best describes the relationship between the stopping potential $$V_{\text{stop}}$$ and the frequency $$f of $$incident light in the photoelectric effect?

$$V_{\text{stop}} = \dfrac{h}{e}(f - f_0$)$$

Question 1

Which of the following best describes the concept of quantization as it applies to energy in atomic systems?

Accepted Answer

Energy can only take on certain discrete values, called quantum states.

Question 2

According to the photon model of light, what is the energy of a single photon with frequency $$f$$?

Accepted Answer

$$E = hf$$

Question 3

A metal has a work function $$E_0 = 4.28$$\ 	ext{eV}$$. What is the minimum frequency of light required to eject electrons from this metal? (Planck's constant h = 4.14$$ 	imes $$10^{-15}$$\ 	ext{eV} \cdot 	ext{s}$$)

Accepted Answer

$$f_0 = 1.03$$ 	imes $$10^{15}$$\ 	ext{Hz}$$

Question 4

Which experimental observation cannot be explained by the classical wave theory of light, but is explained by the photon model?

Accepted Answer

The existence of a threshold frequency in the photoelectric effect.

Question 5

A red laser pointer emits light at $$\lambda = 650\ 	ext{nm}$$ with a power of $$2.0\ 	ext{mW}. $$How many photons does it emit per second? (Use $$h = 6.63 	imes 10$$^{-34}$$\ 	ext{J} \cdot 	ext{s}$$, $$c = 3.00 	imes 10^8$\ 	ext{m/s})$$

Accepted Answer

$$6.5 	imes 10$$^{15}$$ photons/s

Question 6

What is the de Broglie wavelength of an electron (mass $$9.11 	imes 10$$^{-31}$$\ 	ext{kg}) $$moving at $$2.0 	imes 10^6$\ 	ext{m/s}$$? (Planck's constant $$h = 6.63 	imes 10$$^{-34}$$\ 	ext{J} \cdot 	ext{s})$$

Accepted Answer

$$3.6 	imes 10$$^{-10}$$\ 	ext{m}$$

Question 7

In the Bohr model of the hydrogen atom, what is the energy of the electron in the $$nth $$stationary state?

Accepted Answer

$$E_n = -\dfrac{13.60\ 	ext{eV}}{n^2$}$$

Question 8

A photon is emitted when an electron in a hydrogen atom transitions from $$n=3 to$$ $$n=2. $$What is the wavelength of the emitted photon? (Use $$E_n = -13.60\ 	ext{eV}/n^2$, hc = 1240$$\ 	ext{eV} \cdot 	ext{nm}$$)

Accepted Answer

$$656\ 	ext{nm}$$

Question 9

Which statement about the photoelectric effect is correct?

Accepted Answer

Increasing the intensity of light increases the number of emitted electrons, but not their maximum kinetic energy.

Question 10

A particle of mass $$m is $$confined in a one-dimensional box of length $$L. $$What are the allowed energy levels for the particle?

Accepted Answer

$$E_n = \dfrac{n^2$ h^2$}{8mL^2$}$$, $$n=1,2,3,...$$

Question 11

Which of the following best describes the relationship between the stopping potential $$V_{	ext{stop}}$$ and the frequency $$f of $$incident light in the photoelectric effect?

Accepted Answer

$$V_{	ext{stop}} = \dfrac{h}{e}(f - f_0$)$$

Question 12

Which of the following is a consequence of the wave-like nature of matter?

Accepted Answer

Electrons can produce interference patterns in a double-slit experiment.

Question 13

If a photon has a wavelength of $$500\ 	ext{nm}$$, what is its momentum? (Planck's constant $$h = 6.63 	imes 10$$^{-34}$$\ 	ext{J} \cdot 	ext{s})$$

Accepted Answer

$$1.33 	imes 10$$^{-27}$$\ 	ext{kg} \cdot 	ext{m/s}$$

Question 14

Which of the following statements about the Bohr model of the atom is correct?

Accepted Answer

Electrons can only occupy certain discrete orbits with quantized energies.

Question 15

A photon with energy $$3.0\ 	ext{eV}$$ strikes a metal with work function $$2.0\ 	ext{eV}. $$What is the maximum kinetic energy of the emitted electron?

Accepted Answer

$$1.0\ 	ext{eV}$$

Question 16

Which of the following is NOT a postulate of the photon model of light?

Accepted Answer

A photon can deliver part of its energy to multiple electrons.

Question 17

What is the physical meaning of the work function $$E_0 in $$the context of the photoelectric effect?

Accepted Answer

It is the minimum energy required to remove an electron from the metal.

Question 18

Which of the following best explains why the photoelectric effect supports the particle theory of light?

Accepted Answer

Electrons are emitted only when the incident light has a frequency above a certain threshold, regardless of intensity.

Chapter 38: Quantization – Study Notes for Physics for Scientists and Engineers

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