Photoelectric Effect Examples: 44 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Photoelectric Effect.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The photoelectric effect is the emission of electrons from a material when light of high enough frequency shines on it.

Light can hit a surface like tiny packets of energy and knock electrons out.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Photoelectric Effect asks whether the system is nuclear, quantum, or relativistic before using an everyday model.

Common stuck point: Students often know a formula related to photoelectric effect but skip the recognition step: Does the situation involve particles, nuclei, photons, or relativistic speeds where everyday mechanics is not enough? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Does the situation involve particles, nuclei, photons, or relativistic speeds where everyday mechanics is not enough?

Worked Examples

Example 1

medium

A photon of frequency

1.0\times10^{15}\text{ Hz}

strikes sodium (

\phi = 3.65\times10^{-19}\text{ J}

). Find

KE_{\max}

. (

h = 6.6\times10^{-34}

)

Answer

K E_{\max} \approx 2.95 \times 10^{- 19} J

First step

E_\text{photon} = hf = (6.6\times10^{-34})(1.0\times10^{15}) = 6.6\times10^{-19}\text{ J}

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Example 2

medium

A photon of wavelength

300\text{ nm}

strikes a metal with

\phi = 3.0\times10^{-19}\text{ J}

. Find

KE_{\max}

. (

h = 6.6\times10^{-34}

c = 3\times10^8

)

Example 3

medium

A photon of

E = 5.0\text{ eV}

hits a metal with

\phi = 2.0\text{ eV}

. Find

KE_{\max}

in joules (

1\text{ eV} = 1.6\times10^{-19}\text{ J}

Example 4

hard

A photon of frequency

1.5\times10^{15}\text{ Hz}

ejects an electron from a metal of

\phi = 4.0\times10^{-19}\text{ J}

. Find the electron's maximum speed (

h = 6.6\times10^{-34}

m_e = 9.1\times10^{-31}\text{ kg}

Example 5

hard

Light of frequency

2 f_0

hits a metal with threshold

f_0

. Express

KE_{\max}

in terms of

\phi

Example 6

challenge

In a Millikan-style experiment, stopping voltages are

V_1 = 0.5\text{ V}

f_1 = 5\times10^{14}\text{ Hz}

and

V_2 = 1.5\text{ V}

f_2 = 7.5\times10^{14}\text{ Hz}

. Find Planck's constant. (

e = 1.6\times10^{-19}\text{ C}

)

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

Find the energy of a photon of frequency

f = 5\times10^{14} \text{ Hz}

. (

h = 6.6\times10^{-34}

)

Example 2

easy

In the photoelectric effect, electrons are emitted only when light has a high enough what?

Example 3

easy

Write the photoelectric equation relating photon energy, work function, and maximum kinetic energy.

Example 4

easy

If a metal's work function is

\phi = 3\times10^{-19} \text{ J}

and a photon delivers

5\times10^{-19} \text{ J}

, find the maximum kinetic energy of the electron.

Example 5

easy

Does increasing the brightness (intensity) of light below the threshold frequency cause electron emission?

Example 6

easy

Above the threshold, does increasing intensity increase the number or the energy of emitted electrons?

Example 7

easy

Find the threshold frequency for a metal with work function

\phi = 3.3\times10^{-19} \text{ J}

. (

h = 6.6\times10^{-34}

)

Example 8

easy

In the photoelectric effect, light behaves more like a wave or like particles (photons)?

Example 9

medium

A photon of frequency

8\times10^{14} \text{ Hz}

hits a metal with work function

3.3\times10^{-19} \text{ J}

. Find

KE_{\max}

. (

h = 6.6\times10^{-34}

)

Example 10

medium

A metal has threshold frequency

4\times10^{14} \text{ Hz}

. Find its work function. (

h = 6.6\times10^{-34}

)

Example 11

medium

The stopping potential for ejected electrons is

1.5 \text{ V}

. Find their maximum kinetic energy (

e = 1.6\times10^{-19} \text{ C}

Example 12

medium

A photon has wavelength

\lambda = 4\times10^{-7} \text{ m}

. Find its energy. (

h = 6.6\times10^{-34}

c = 3\times10^8

)

Example 13

medium

Light of energy

6\times10^{-19} \text{ J}

ejects electrons with

KE_{\max} = 2\times10^{-19} \text{ J}

. Find the work function.

Example 14

medium

Two metals have work functions

\phi_1 = 2\times10^{-19}

and

\phi_2 = 5\times10^{-19} \text{ J}

. For the same photon energy, which emits faster electrons?

Example 15

medium

A photon of frequency

6 imes10^{14} ext{ Hz}

hits a metal with work function

2.6 imes10^{-19} ext{ J}

. Find

KE_{\max}

. (

h = 6.6 imes10^{-34}

)

Example 16

medium

A metal emits electrons with

KE_{\max} = 1.4 imes10^{-19} ext{ J}

under a photon of

4 imes10^{-19} ext{ J}

. Find the work function.

Example 17

medium

The stopping potential is

2 ext{ V}

. Find the maximum kinetic energy of the electrons (

e = 1.6 imes10^{-19} ext{ C}

Example 18

challenge

A photon of

7\times10^{-19} \text{ J}

hits a metal with

\phi = 4\times10^{-19} \text{ J}

. Find the electron's maximum speed (

m_e = 9.1\times10^{-31} \text{ kg}

Example 19

challenge

Light of wavelength

3\times10^{-7} \text{ m}

strikes a metal with work function

4\times10^{-19} \text{ J}

. Find

KE_{\max}

. (

h = 6.6\times10^{-34}

c = 3\times10^8

)

Example 20

challenge

Photon energy

E

just exceeds work function

\phi

KE_{\max} = 0.1\phi

. Express

E

in terms of

\phi

Example 21

easy

Find the energy of a photon with frequency

f = 6\times10^{14}\text{ Hz}

. (

h = 6.6\times10^{-34}

)

Example 22

easy

The work function of a metal is

4.5\times10^{-19}\text{ J}

. Find its threshold frequency. (

h = 6.6\times10^{-34}

)

Example 23

easy

A metal has

\phi = 3.0\times10^{-19}\text{ J}

. A photon arrives with

E = 5.0\times10^{-19}\text{ J}

. Find

KE_{\max}

Example 24

easy

Express the work function

\phi = 4.8\times10^{-19}\text{ J}

in electronvolts. (

1\text{ eV} = 1.6\times10^{-19}\text{ J}

)

Example 25

easy

A photon has wavelength

\lambda = 500\text{ nm}

. Find its energy. (

h = 6.6\times10^{-34}

c = 3\times10^8

)

Example 26

medium

The stopping voltage for ejected electrons is

V_s = 0.8\text{ V}

. Find their maximum kinetic energy (

e = 1.6\times10^{-19}\text{ C}

Example 27

medium

A metal emits electrons with

KE_{\max} = 1.5\times10^{-19}\text{ J}

under light of

f = 7\times10^{14}\text{ Hz}

. Find

\phi

. (

h = 6.6\times10^{-34}

)

Example 28

medium

A metal has threshold wavelength

\lambda_0 = 500\text{ nm}

. Find its work function. (

h = 6.6\times10^{-34}

c = 3\times10^8

)

Example 29

medium

Find the threshold wavelength for a metal with

\phi = 6.0\times10^{-19}\text{ J}

. (

h = 6.6\times10^{-34}

c = 3\times10^8

)

Example 30

medium

A photon ejects an electron with

KE_{\max} = 4.0\times10^{-19}\text{ J}

. Find the stopping voltage (

e = 1.6\times10^{-19}\text{ C}

Example 31

medium

A graph of

KE_{\max}

versus

f

has slope

h

and

y

-intercept

-\phi

. If the slope is

6.6\times10^{-34}\text{ J s}

and intercept is

-3.3\times10^{-19}\text{ J}

, find the threshold frequency.

Example 32

medium

Two metals have

\phi_A = 2.0\text{ eV}

and

\phi_B = 4.0\text{ eV}

. Identical photons of

E = 5.0\text{ eV}

hit each. Which emits faster electrons?

Example 33

medium

A laser delivers

1\times10^{18}

photons per second of energy

4\times10^{-19}\text{ J}

each. Find the laser's power.

Example 34

hard

A photon of

\lambda = 250\text{ nm}

hits a metal with threshold wavelength

\lambda_0 = 350\text{ nm}

. Find

KE_{\max}

. (

h = 6.6\times10^{-34}

c = 3\times10^8

)

Example 35

hard

A photon ejects an electron whose stopping voltage is

1.2\text{ V}

. The metal's work function is

3.0\times10^{-19}\text{ J}

. Find the photon frequency (

h = 6.6\times10^{-34}

e = 1.6\times10^{-19}\text{ C}

Example 36

hard

A metal of work function

\phi = 2.8\times10^{-19}\text{ J}

is illuminated with light of

\lambda = 400\text{ nm}

. Will electrons be emitted? (

h = 6.6\times10^{-34}

c = 3\times10^8

)

Example 37

hard

A photoelectric cell is illuminated by red light (

f = 4\times10^{14}\text{ Hz}

) and ejected electrons have

KE_{\max} = 1.0\times10^{-19}\text{ J}

. The light is replaced with blue light of

f = 7\times10^{14}\text{ Hz}

. Find the new

KE_{\max}

. (

h = 6.6\times10^{-34}

)

Example 38

challenge

Light of

\lambda = 200\text{ nm}

shines on a metal with

\phi = 3.0\text{ eV}

. Find

KE_{\max}

in eV. (

h = 6.6\times10^{-34}

c = 3\times10^8

1\text{ eV} = 1.6\times10^{-19}\text{ J}

)

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Related Concepts

Visible Light Frequency Special Relativity

Background Knowledge

These ideas may be useful before you work through the harder examples.

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