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7.6 Photoelectric Effect

6 min readmay 10, 2023

S

Saarah Hasan

Daniella Garcia-Loos

Daniella Garcia-Loos

S

Saarah Hasan

Daniella Garcia-Loos

Daniella Garcia-Loos

Photoelectric Effect

The idea that light exhibits particle properties was first suggested by when he showed that light transferred energy just like a particle(E=mc^2). expanded the groundwork of this idea further in 1923 when he showed that light has momentum and can undergo elastic collisions. From multiple physicists' work, we now know that light behaves like a stream of , which can be illustrated by the :

The is the phenomenon in which electrons are emitted from a metal surface when it is exposed to light.

Here are some key points about the at an AP Physics level:

  • The is the phenomenon in which electrons are emitted from a metal surface when it is exposed to light. It is an important concept in physics and is used to understand the behavior of electrons in materials and to predict the behavior of physical phenomena.
  • The occurs when light of a high enough frequency is shone on a metal surface. The light causes the electrons in the metal to be excited and to be emitted from the surface.
  • The energy of the emitted electrons is dependent on the frequency of the light, but not on the intensity of the light. This is known as the relationship.
  • The is an important concept in and is used to understand the behavior of electrons in materials and to predict the behavior of physical phenomena. It is also used in a variety of applications, including , , and .

When light shines on a piece of metal, some of the enter the surface of the metal, collide with the atoms and get absorbed, giving energy to the metal’s surface electrons. If this energy is great enough, the electrons can jump from their bound state and fly off. These electrons that break free are known as photo-electrons.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-AZUhfUtw0Jeh.png?alt=media&token=2ba9cbae-f7b9-4f09-b048-6f948c1caed5

Taken from Wikimedia Commons

  1. There would be a large time delay between the point when the light shined on the metal and when the electrons would break off.
  2. Increasing the would cause the photo-electrons to be ejected with greater kinetic energy, since a wave’s energy is related to its intensity.
  3. All frequencies of light would cause photoelectrons to eject, as long as the intensity was high enough.

What actually happened:

  1. Electrons broke off within a few billionths of a second after getting shined on.
  2. Increasing the didn’t increase the photoelectron’s kinetic energy. More electrons flew off as the intensity increased, but there was a certain maximum photoelectron kinetic energy.
  3. For each metal, there was a specific threshold frequency, f0​. If the light’s frequency was lower than the f0​, then no electrons flew off. The intensity of the light wasn’t a factor.

The energy of a photon can be found by:

E=hf

where h = Plancks constant = 6.63 ∗ 10^−34 J*s

f = frequency

Remember that:

f=c/λ

E=hf➡️

E=hc/λ

In order for the metal’s surface electrons to break free, a certain amount of energy has to be transferred to them. This is known as the metal’s work function(Φ). If an electron absorbed a photon with an energy (E) greater than Φ, then it would eject with a maximum kinetic energy of: K(max)=E-Φ ➡️ Kmax= hf-Φ

The threshold frequency can be expressed as: f_0=Φ/h

Some things to keep in mind:

  • The kinetic energy of the photoelectrons is independent of the .
  • The greater the light’s intensity, the more electrons ejected, hence the current increases.

Practice Problems:

1. Light of a single frequency falls on a photoelectric material but no electrons are emitted. Electrons may be emitted if the A) frequency of light is decreased

B) frequency of light is increased

C) is decreased

D) is increased

E) velocity of light is increased

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-mDRcRmSmF7Zu.png?alt=media&token=f74cfa63-4e75-42f0-9255-4a170d78b006

2. A student performs the experiment and obtains the data depicted in the accompanying graph of Ek​m​ (max kinetic energy) of photo-electrons vs the frequency of the . What is the approximate work function of this material?

A) 1.5 eV

B) 2.0 eV

C) 2.7 eV

D) 4.0 eV

E) 6.0 eV

3. Which graph best shows the maximum kinetic energy K of the photoelectrons as a function of the frequency of incident light? A) A

B) B

C) C

D) D

E) E

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-gfMHIQorPtjX.png?alt=media&token=bd0ab50e-e8b1-4d5b-8313-302232bc07a3

4. Which graph best shows the maximum kinetic energy K of a photo-electron as a function of the intensity of incident light? A) A

B) B

C) C

D) D

E) E

5. In the , the maximum speed of the electrons emitted by a metal surface when it is illuminated by light depends on which of the following? I. Intensity of the light II. Frequency of the light III. Nature of the photoelectric surface A) I only

B) III only

C) I and II only

D) II and III only

E) I, II, and III


Answers:

  1. B: Standard question. If the frequency does not cause emission, it is below the threshold and will not be able to cause emission. The only way to cause emission is the increase the frequency above the threshold.

  2. A: From K = hf – ϕ … y = mx + b … the work function is the y-intercept, extend the line

  3. A: Below a threshold frequency, there would be no emissions and thus zero K for everything below that point. Above that threshold, more frequency means more K based on K = hf – ϕ, with h as the constant slope. Graph A has all these properties.

  4. E: Intensity has no effect on the energy of a single given photo-electron. Each photo-electron’s energy is simply based on K = hf – ϕ. More intensity means a larger total number of photo-electrons and would result in more total energy, but the energy of each photo-electron is the same for all levels of the overall intensity.

  5. D: Intensity has no effect on the energy of a single given photo-electron. Each photo-electron’s energy is simply based on K = hf – ϕ. More intensity means a larger total number of photo-electrons and would result in more total energy, but the energy of each photo-electron is the same for all levels of the overall intensity. K is based on the work function (which is based on the nature of the surface) and K is also based on the frequency of the incoming light.

  6. B: The K of each photo-electron is given by. K = hf – ϕ. To reduce the energy of each photon, we need less f (which means more λ) for the incoming light. Since intensity is directly related to the number of photo-electrons emitted we want to increase the intensity.

Key Terms to Review (16)

Compton

: Compton scattering is an interaction between photons and charged particles such as electrons. It involves a change in wavelength or frequency due to photon-electron collisions, providing evidence for both wave-like and particle-like properties of light.

Detectors

: Detectors are devices used to measure or detect various physical quantities such as light intensity, radiation levels, temperature, or electric current.

Einstein

: Albert Einstein was a renowned physicist who developed many groundbreaking theories, including his theory of relativity and his explanation of the photoelectric effect. He revolutionized our understanding of space, time, and energy.

Frequency (f)

: Frequency refers to the number of complete cycles or oscillations per unit time. In physics, it specifically refers to the number of wave crests passing through a given point per second.

Intensity of light

: Intensity refers to the amount of power per unit area carried by light waves. It represents how bright or dim light appears.

Kinetic energy (Kmax)

: Kinetic energy refers to the energy possessed by an object due to its motion.

Lasers

: Lasers are devices that produce a narrow, intense beam of coherent light through the process of stimulated emission.

Photoelectric Effect

: The photoelectric effect is the phenomenon where electrons are emitted from a material when it absorbs photons (light particles) with sufficient energy. It demonstrates that light behaves as both a particle and a wave.

Photons

: Photons are particles of light that carry energy and have zero mass. They behave both as particles and waves, and their energy is directly proportional to their frequency.

Planck's Constant

: Planck's constant (symbolized as h) is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency. It is used to calculate the energy levels and behavior of particles at the atomic and subatomic scale.

Quantum Mechanics

: Quantum mechanics is a branch of physics that deals with the behavior of particles at the atomic and subatomic level, where classical physics fails to explain their properties accurately.

Solar cells

: Solar cells are devices made from semiconductor materials that convert sunlight directly into electricity through the photovoltaic effect.

Speed of light (c)

: The speed of light is the fastest possible speed at which energy or information can travel in a vacuum. It is approximately 299,792,458 meters per second.

Threshold frequency (f_0)

: The threshold frequency is the minimum frequency of light required to eject electrons from a metal surface in the photoelectric effect.

Wavelength (λ)

: Wavelength refers to the distance between two consecutive points on a wave that are in phase with each other. It is usually measured from crest to crest or trough to trough.

Work function (Φ)

: Work function refers to the minimum amount of energy required for an electron to escape from the surface of a material and become free.

7.6 Photoelectric Effect

6 min readmay 10, 2023

S

Saarah Hasan

Daniella Garcia-Loos

Daniella Garcia-Loos

S

Saarah Hasan

Daniella Garcia-Loos

Daniella Garcia-Loos

Photoelectric Effect

The idea that light exhibits particle properties was first suggested by when he showed that light transferred energy just like a particle(E=mc^2). expanded the groundwork of this idea further in 1923 when he showed that light has momentum and can undergo elastic collisions. From multiple physicists' work, we now know that light behaves like a stream of , which can be illustrated by the :

The is the phenomenon in which electrons are emitted from a metal surface when it is exposed to light.

Here are some key points about the at an AP Physics level:

  • The is the phenomenon in which electrons are emitted from a metal surface when it is exposed to light. It is an important concept in physics and is used to understand the behavior of electrons in materials and to predict the behavior of physical phenomena.
  • The occurs when light of a high enough frequency is shone on a metal surface. The light causes the electrons in the metal to be excited and to be emitted from the surface.
  • The energy of the emitted electrons is dependent on the frequency of the light, but not on the intensity of the light. This is known as the relationship.
  • The is an important concept in and is used to understand the behavior of electrons in materials and to predict the behavior of physical phenomena. It is also used in a variety of applications, including , , and .

When light shines on a piece of metal, some of the enter the surface of the metal, collide with the atoms and get absorbed, giving energy to the metal’s surface electrons. If this energy is great enough, the electrons can jump from their bound state and fly off. These electrons that break free are known as photo-electrons.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-AZUhfUtw0Jeh.png?alt=media&token=2ba9cbae-f7b9-4f09-b048-6f948c1caed5

Taken from Wikimedia Commons

  1. There would be a large time delay between the point when the light shined on the metal and when the electrons would break off.
  2. Increasing the would cause the photo-electrons to be ejected with greater kinetic energy, since a wave’s energy is related to its intensity.
  3. All frequencies of light would cause photoelectrons to eject, as long as the intensity was high enough.

What actually happened:

  1. Electrons broke off within a few billionths of a second after getting shined on.
  2. Increasing the didn’t increase the photoelectron’s kinetic energy. More electrons flew off as the intensity increased, but there was a certain maximum photoelectron kinetic energy.
  3. For each metal, there was a specific threshold frequency, f0​. If the light’s frequency was lower than the f0​, then no electrons flew off. The intensity of the light wasn’t a factor.

The energy of a photon can be found by:

E=hf

where h = Plancks constant = 6.63 ∗ 10^−34 J*s

f = frequency

Remember that:

f=c/λ

E=hf➡️

E=hc/λ

In order for the metal’s surface electrons to break free, a certain amount of energy has to be transferred to them. This is known as the metal’s work function(Φ). If an electron absorbed a photon with an energy (E) greater than Φ, then it would eject with a maximum kinetic energy of: K(max)=E-Φ ➡️ Kmax= hf-Φ

The threshold frequency can be expressed as: f_0=Φ/h

Some things to keep in mind:

  • The kinetic energy of the photoelectrons is independent of the .
  • The greater the light’s intensity, the more electrons ejected, hence the current increases.

Practice Problems:

1. Light of a single frequency falls on a photoelectric material but no electrons are emitted. Electrons may be emitted if the A) frequency of light is decreased

B) frequency of light is increased

C) is decreased

D) is increased

E) velocity of light is increased

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-mDRcRmSmF7Zu.png?alt=media&token=f74cfa63-4e75-42f0-9255-4a170d78b006

2. A student performs the experiment and obtains the data depicted in the accompanying graph of Ek​m​ (max kinetic energy) of photo-electrons vs the frequency of the . What is the approximate work function of this material?

A) 1.5 eV

B) 2.0 eV

C) 2.7 eV

D) 4.0 eV

E) 6.0 eV

3. Which graph best shows the maximum kinetic energy K of the photoelectrons as a function of the frequency of incident light? A) A

B) B

C) C

D) D

E) E

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-gfMHIQorPtjX.png?alt=media&token=bd0ab50e-e8b1-4d5b-8313-302232bc07a3

4. Which graph best shows the maximum kinetic energy K of a photo-electron as a function of the intensity of incident light? A) A

B) B

C) C

D) D

E) E

5. In the , the maximum speed of the electrons emitted by a metal surface when it is illuminated by light depends on which of the following? I. Intensity of the light II. Frequency of the light III. Nature of the photoelectric surface A) I only

B) III only

C) I and II only

D) II and III only

E) I, II, and III


Answers:

  1. B: Standard question. If the frequency does not cause emission, it is below the threshold and will not be able to cause emission. The only way to cause emission is the increase the frequency above the threshold.

  2. A: From K = hf – ϕ … y = mx + b … the work function is the y-intercept, extend the line

  3. A: Below a threshold frequency, there would be no emissions and thus zero K for everything below that point. Above that threshold, more frequency means more K based on K = hf – ϕ, with h as the constant slope. Graph A has all these properties.

  4. E: Intensity has no effect on the energy of a single given photo-electron. Each photo-electron’s energy is simply based on K = hf – ϕ. More intensity means a larger total number of photo-electrons and would result in more total energy, but the energy of each photo-electron is the same for all levels of the overall intensity.

  5. D: Intensity has no effect on the energy of a single given photo-electron. Each photo-electron’s energy is simply based on K = hf – ϕ. More intensity means a larger total number of photo-electrons and would result in more total energy, but the energy of each photo-electron is the same for all levels of the overall intensity. K is based on the work function (which is based on the nature of the surface) and K is also based on the frequency of the incoming light.

  6. B: The K of each photo-electron is given by. K = hf – ϕ. To reduce the energy of each photon, we need less f (which means more λ) for the incoming light. Since intensity is directly related to the number of photo-electrons emitted we want to increase the intensity.

Key Terms to Review (16)

Compton

: Compton scattering is an interaction between photons and charged particles such as electrons. It involves a change in wavelength or frequency due to photon-electron collisions, providing evidence for both wave-like and particle-like properties of light.

Detectors

: Detectors are devices used to measure or detect various physical quantities such as light intensity, radiation levels, temperature, or electric current.

Einstein

: Albert Einstein was a renowned physicist who developed many groundbreaking theories, including his theory of relativity and his explanation of the photoelectric effect. He revolutionized our understanding of space, time, and energy.

Frequency (f)

: Frequency refers to the number of complete cycles or oscillations per unit time. In physics, it specifically refers to the number of wave crests passing through a given point per second.

Intensity of light

: Intensity refers to the amount of power per unit area carried by light waves. It represents how bright or dim light appears.

Kinetic energy (Kmax)

: Kinetic energy refers to the energy possessed by an object due to its motion.

Lasers

: Lasers are devices that produce a narrow, intense beam of coherent light through the process of stimulated emission.

Photoelectric Effect

: The photoelectric effect is the phenomenon where electrons are emitted from a material when it absorbs photons (light particles) with sufficient energy. It demonstrates that light behaves as both a particle and a wave.

Photons

: Photons are particles of light that carry energy and have zero mass. They behave both as particles and waves, and their energy is directly proportional to their frequency.

Planck's Constant

: Planck's constant (symbolized as h) is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency. It is used to calculate the energy levels and behavior of particles at the atomic and subatomic scale.

Quantum Mechanics

: Quantum mechanics is a branch of physics that deals with the behavior of particles at the atomic and subatomic level, where classical physics fails to explain their properties accurately.

Solar cells

: Solar cells are devices made from semiconductor materials that convert sunlight directly into electricity through the photovoltaic effect.

Speed of light (c)

: The speed of light is the fastest possible speed at which energy or information can travel in a vacuum. It is approximately 299,792,458 meters per second.

Threshold frequency (f_0)

: The threshold frequency is the minimum frequency of light required to eject electrons from a metal surface in the photoelectric effect.

Wavelength (λ)

: Wavelength refers to the distance between two consecutive points on a wave that are in phase with each other. It is usually measured from crest to crest or trough to trough.

Work function (Φ)

: Work function refers to the minimum amount of energy required for an electron to escape from the surface of a material and become free.


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AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.


© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.