Q: Which equation correctly expresses the photoelectric effect at the cutoff wavelength?

$$KE_{\text{max}} = 0 = \frac{hc}{\lambda_c} - \phi$$

Q: Given a work function $$\phi = 6.35\ \text{eV}$$, what is the cutoff frequency $$f_c$$?

$$f_c = 1.53 \times 10$$^{15}$$\ \text{Hz}$$

Q: A photon with wavelength $$400\ \text{nm} is $$incident on a material. What is the energy of the photon?

$$E_{\text{photon}} = 3.11\ \text{eV}$$

Q: Given $$KE_{\text{max}} = 2.50\ \text{eV}$$, what is the maximum speed $$v_{\text{max}} of $$the emitted electrons? ($$m_e = 9.11 \times 10$$^{-31}$$\ \text{kg}$$, $$1\ \text{eV} = 1.60 \times 10$$^{-19}$$\ \text{J})$$

$$v_{\text{max}} = 9.37 \times 10^5$\ \text{m/s}$$

Question 1

Which equation correctly expresses the photoelectric effect at the cutoff wavelength?

Accepted Answer

$$KE_{	ext{max}} = 0 = \frac{hc}{\lambda_c} - \phi$$

Question 2

Given a work function $$\phi = 2.24\ 	ext{eV}$$, what is the cutoff wavelength $$\lambda_c$$ for the photoelectric effect? (Use $$h = 6.63 	imes 10$$^{-34}$$\ 	ext{J} \cdot 	ext{s}$$, $$c = 3.00 	imes 10^8$\ 	ext{m/s}$$, $$1\ 	ext{eV} = 1.60 	imes 10$$^{-19}$$\ 	ext{J})$$

Accepted Answer

$$\lambda_c = 555\ 	ext{nm}$$

Question 3

If the cutoff wavelength for a material is $$288\ 	ext{nm}$$, what is the corresponding work function $$\phi$$?

Accepted Answer

$$\phi = 4.31\ 	ext{eV}$$

Question 4

A photon with energy $$5.50\ 	ext{eV}$$ strikes a surface with work function $$4.31\ 	ext{eV}. $$What is the maximum kinetic energy of the emitted electrons?

Accepted Answer

$$1.19\ 	ext{eV}$$

Question 5

What is the stopping potential $$V_s if $$the maximum kinetic energy of photoelectrons is $$2.15\ 	ext{eV}$$?

Accepted Answer

$$V_s = 2.15\ 	ext{V}$$

Question 6

Given a work function $$\phi = 6.35\ 	ext{eV}$$, what is the cutoff frequency $$f_c$$?

Accepted Answer

$$f_c = 1.53 	imes 10$$^{15}$$\ 	ext{Hz}$$

Question 7

If the cutoff frequency for a material is $$1.53 	imes 10$$^{15}$$\ 	ext{Hz}$$, what is the cutoff wavelength $$\lambda_c$$?

Accepted Answer

$$\lambda_c = 196\ 	ext{nm}$$

Question 8

A photon with wavelength $$400\ 	ext{nm} is $$incident on a material. What is the energy of the photon?

Accepted Answer

$$E_{	ext{photon}} = 3.11\ 	ext{eV}$$

Question 9

If the stopping potential is $$0.216\ 	ext{V}$$, what is the maximum kinetic energy of the photoelectrons?

Accepted Answer

$$0.216\ 	ext{eV}$$

Question 10

Given $$KE_{	ext{max}} = 2.50\ 	ext{eV}$$, what is the maximum speed $$v_{	ext{max}} of $$the emitted electrons? ($$m_e = 9.11 	imes 10$$^{-31}$$\ 	ext{kg}$$, $$1\ 	ext{eV} = 1.60 	imes 10$$^{-19}$$\ 	ext{J})$$

Accepted Answer

$$v_{	ext{max}} = 9.37 	imes 10^5$\ 	ext{m/s}$$

Question 11

If the work function of silver is $$4.73\ 	ext{eV}$$ and the maximum kinetic energy of photoelectrons is $$2.50\ 	ext{eV}$$, what is the wavelength of the incident light?

Accepted Answer

$$\lambda = 172\ 	ext{nm}$$

Question 12

A material has a work function $$\phi = 1.90\ 	ext{eV}. If $$the incident light has a wavelength of $$546.1\ 	ext{nm}$$ and the maximum kinetic energy of the emitted electrons is $$0.376\ 	ext{eV}$$, what is the energy of the incident photon?

Accepted Answer

Question 13

Which of the following best describes the relationship between the stopping potential $$V_s$$ and the maximum kinetic energy $$KE_{	ext{max}} of $$photoelectrons?

Accepted Answer

$$eV_s = KE_{	ext{max}}$$

Question 14

A graph of $$KE_{	ext{max}} vs. $$frequency $$f$$ for a photoelectric material is shown. What does the slope of the linear portion of the graph represent?

Accepted Answer

Planck's constant $$h$$

Question 15

If the frequency of incident light is below the cutoff frequency $$f_c$$, what happens to the emission of photoelectrons?

Accepted Answer

No photoelectrons are emitted.

Question 16

If the wavelength of incident light is decreased (while keeping intensity constant), what happens to the maximum kinetic energy of the emitted photoelectrons?

Accepted Answer

It increases.

Question 17

Which of the following is the correct expression for the energy of a photon in terms of its wavelength?

Accepted Answer

$$E = \frac{hc}{\lambda}$$

Photoelectric Effect: Concepts, Equations, and Applications

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