Photoelectric Effect

Introduction: What is the Photoelectric Effect and Why does it Occur?

The photoelectric effect is a phenomenon in which electrons are ejected from the surface of a metal when light is incident on it. These ejected electrons are called photoelectrons. It is important to note that the emission of photoelectrons and the kinetic energy of the ejected photoelectrons is dependent on the frequency of the light that is incident on the metal’s surface. The process through which photoelectrons are ejected from the surface of the metal due to the action of light is commonly referred to as photoemission.

The photoelectric effect occurs because the electrons at the surface of the metal tend to absorb energy from the incident light and use it to overcome the attractive forces that bind them to the metallic nuclei. An illustration detailing the emission of photoelectrons as a result of the photoelectric effect is provided below.

Photoelectric Effect

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IntroductionHistory of the Photoelectric EffectPrincipleFormulaLaws Governing the Photoelectric EffectExperimental Study of the Photoelectric EffectEinstien’s Photoelectric EquationGraphsApplicationsSolved Problems (Numericals)

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Explaining the Photoelectric Effect: The Concept of Photons

The photoelectric effect cannot be explained by considering light as a wave. However, this phenomenon can be explained by the particle nature of light, in which light can be visualized as a stream of particles of electromagnetic energy. These ‘particles’ of light are called photons. The energy held by a photon is related to the frequency of the light via Planck’s equation:

E = h𝜈 = hc/λ

Where,

  • E denotes the energy of the photon
  • h is Planck’s constant
  • 𝜈 denotes the frequency of the light
  • c is the speed of light (in a vacuum)
  • λ is the wavelength of the light

Thus, it can be understood that different frequencies of light carry photons of varying energies. For example, the frequency of blue light is greater than that of red light (the wavelength of blue light is much shorter than the wavelength of red light). Therefore, the energy held by a photon of blue light will be greater than the energy held by a photon of red light.

Threshold Energy for the Photoelectric Effect

For the photoelectric effect to occur, the photons that are incident on the surface of the metal must carry sufficient energy to overcome the attractive forces that bind the electrons to the nuclei of the metals. The minimum amount of energy required to remove an electron from the metal is called the threshold energy (denoted by the symbol Φ). For a photon to possess energy equal to the threshold energy, its frequency must be equal to the threshold frequency (which is the minimum frequency of light required for the photoelectric effect to occur). The threshold frequency is usually denoted by the symbol 𝜈th and the associated wavelength (called the threshold wavelength) is denoted by the symbol λth. The relationship between the threshold energy and the threshold frequency can be expressed as follows.

Φ = h𝜈th = hc/λth

Relationship between the Frequency of the Incident Photon and the Kinetic Energy of the Emitted Photoelectron

Therefore, the relationship between the energy of the photon and the kinetic energy of the emitted photoelectron can be written as follows.

Ephoton = Φ + Eelectron

⇒ h𝜈 = h𝜈th + ½mev2

Where,

  • Ephoton denotes the energy of the incident photon, which is equal to h𝜈
  • Φ denotes the threshold energy of the metal surface, which is equal to h𝜈th
  • Eelectron denotes the kinetic energy of the photoelectron, which is equal to ½mev2 (me = mass of electron = 9.1*10-31 kg)

If the energy of the photon is less than the threshold energy, there will be no emission of photoelectrons (since the attractive forces between the nuclei and the electrons cannot be overcome). Thus, the photoelectric effect will not occur if 𝜈 < 𝜈th. If the frequency of the photon is exactly equal to the threshold frequency (𝜈 = 𝜈th), there will be an emission of photoelectrons, but their kinetic energy will be equal to zero. An illustration detailing the effect of the frequency of the incident light on the kinetic energy of the photoelectron is provided below.

Relationship between the Frequency of the Incident Photon and the Kinetic Energy of the Emitted Photoelectron

From the image, it can be observed that:

  • The photoelectric effect does not occur when the red light strikes the metallic surface because the frequency of red light is lower than the threshold frequency of the metal.
  • The photoelectric effect occurs when green light strikes the metallic surface and photoelectrons are emitted.
  • The photoelectric effect also occurs when blue light strikes the metallic surface. However, the kinetic energies of the emitted photoelectrons are much higher for blue light than for green light. This is because blue light has a greater frequency than green light.

It is important to note that the threshold energy varies from metal to metal. This is because the attractive forces that bind the electrons to the metal are different for different metals. It can also be noted that the photoelectric effect can also take place in non-metals, but the threshold frequencies of non-metallic substances are usually very high.

History of the Photoelectric Effect

The photoelectric effect was first introduced by Wilhelm Ludwig Franz Hallwachs in the year 1887 and the experimental verification was done by Heinrich Rudolf Hertz. They observed that when a surface is exposed to electromagnetic radiation at a higher threshold frequency, the radiation is absorbed and the electrons are emitted. Today, we study photoelectric effect as a phenomenon which involves a material absorbing electromagnetic radiation and releasing electrically charged particles.

To be more precise, light incident on the surface of a metal in the photoelectric effect causes electrons to be ejected. The electron ejected due to the photoelectric effect is called a photoelectron and is denoted by e. The current produced as a result of the ejected electrons is called photoelectric current.

Einstien’s Contributions towards the Photoelectric Effect

The photoelectric effect is the process that involves the ejection or release of electrons from the surface of materials (generally a metal) when light falls on them. The photoelectric effect is an important concept that enables us to clearly understand the quantum nature of light and electrons.

After continuous research in this field, the explanation for the photoelectric effect was successfully explained by Albert Einstein. He concluded that this effect occurred as a result of light energy being carried in discrete quantized packets. For this excellent work, he was honoured with the Nobel prize in 1921.

According to Einstein, each photon of energy E is

E = hν

Where E = Energy of photon in joule

h = planks constant (6.626 × 10-34 J.s)

ν = frequency of photon in Hz

Properties of the Photon

  • For a photon, all the quantum numbers are zero.
  • A photon does not have any mass, charge and they are not reflected in a magnetic and electric field.
  • The photon moves in the speed of light at empty space.
  • During the interaction of matters with radiation, radiation behaves as it is made up of small particles called photons.
  • Photons are virtual particles. The photon energy is directly proportional to its frequency and inversely proportional to its wavelength.
  • The momentum and energy of the photons are related as given below

E = p.c where

p = magnitude of the momentum

c = speed of light.

Definition of Photoelectric Effect

The phenomenon of metals releasing electrons when they are exposed to the light of the appropriate frequency is called the photoelectric effect, and the electrons emitted during the process are called photoelectrons.

Principle of Photoelectric Effect

The law of conservation of energy forms the basis for the photoelectric effect.

Minimum Condition for Photoelectric Effect

Threshold Frequency (γth)

It is the minimum frequency of the incident light or radiation that will produce a photoelectric effect i.e. ejection of photoelectrons from a metal surface is known as threshold frequency for the metal. It is constant for a specific metal but may be different for different metals.

If γ = frequency of incident photon and γth= threshold frequency, then,

  • If γ < γTh, there will be no ejection of photoelectron and, therefore, no photoelectric effect.
  • If γ = γTh, photoelectrons are just ejected from the metal surface, in this case, the kinetic energy of the electron is zero
  • If γ > γTh, then photoelectrons will come out of the surface along with kinetic energy

Threshold Wavelength (λth)

During the emission of electrons, a metal surface corresponding to the greatest wavelength to incident light is known threshold wavelength.

λth = c/γth

For wavelengths above this threshold, there will be no photoelectron emission. For λ = wavelength of the incident photon, then

  • If λ < λTh, then the photoelectric effect will take place and ejected electron will possess kinetic energy.
  • If λ = λTh, then just photoelectric effect will take place and kinetic energy of ejected photoelectron will be zero.
  • If λ > λTh, there will be no photoelectric effect.

Work Function or Threshold Energy (Φ)

The minimal energy of thermodynamic work that is needed to remove an electron from a conductor to a point in the vacuum immediately outside the surface of the conductor is known as work function/threshold energy

Φ = hγth = hc/λth

The work function is the characteristic of a given metal. If E = energy of an incident photon, then

  1. If E < Φ, no photoelectric effect will take place.
  2. If E = Φ, just photoelectric effect will take place but the kinetic energy of ejected photoelectron will be zero
  3. If E > photoelectron will be zero
  4. If E > Φ, the photoelectric effect will take place along with possession of the kinetic energy by the ejected electron.

Photoelectric Effect Formula

According to the Einstein explanation of the photoelectric effect is:

The energy of photon = energy needed to remove an electron + kinetic energy of the emitted electron

i.e. hν = W + E

Where,

  • h is Planck’s constant.
  • ν is the frequency of the incident photon.
  • W is a work function.
  • E is the maximum kinetic energy of ejected electrons: 1/2 mv².

Laws Governing the Photoelectric Effect

  1. For a light of any given frequency; (γ > γ Th) photoelectric current is directly proportional to the intensity of light
  2. For any given material, there is a certain minimum (energy) frequency, called threshold frequency, below which the emission of photoelectrons stops completely, no matter how high is the intensity of incident light.
  3. The maximum kinetic energy of the photoelectrons is found to increase with the increase in the frequency of incident light, provided the frequency (γ > γ Th) exceeds the threshold limit. The maximum kinetic energy is independent of the intensity of light.
  4. The photo-emission is an instantaneous process.

Experimental Study of Photoelectric Effect

Photoelectric Effect

Photoelectric Effect: Experimental Setup

The given set up D experiment is used to study the photoelectric effect experimentally. In an evacuated glass tube. Two zinc plates C and D are enclosed. Plates C acts as anode and D acts as a photosensitive plate.

Two plates are connected to a battery B and ammeter A. If the radiation is incident on the plate D through a quartz window W electrons are ejected out of the plate and current flows in the circuit this is known as photocurrent. Plate C can be maintained at desired potential (+ve or – ve) with respect to plate D.

Characteristics Of Photoelectric Effect

  • The threshold frequency varies with material, it is different for different materials.
  • The photoelectric current is directly proportional to the light intensity.
  • The kinetic energy of the photoelectrons is directly proportional to the light frequency.
  • The stopping potential is directly proportional to the frequency and the process is instantaneous.

Factors affecting Photoelectric Effect

With the help of this apparatus, we will now study the dependence of the photoelectric effect on the following factors.

  1. The intensity of incident radiation.
  2. A potential difference between metal plate and collector.
  3. Frequency of incident radiation.

Effects of Intensity of Incident Radiation on Photoelectric Effect

The potential difference between the metal plate and collector and frequency of incident light is kept constant and the intensity of light is varied:

The electrode C i.e. collecting electrode is made positive with respect to D (metal plate). For a fixed value of frequency and the potential between the metal plate and collector, the photoelectric current is noted in accordance with the intensity of incident radiation.

It shows that photoelectric current and intensity of incident radiation both are proportional to each other the photoelectric current gives an account of the number of photoelectrons ejected per sec.

Effects of Potential Difference between metal plate and collector on Photoelectric Effect

The frequency of incident light and intensity is kept constant and the potential difference between the plates is varied:

Keeping the intensity and frequency of light constant, the positive potential of C is increased gradually. Photoelectric current increases when there is a positive increase in the potential between the metal plate and collector up to a characteristic value.

There is no change in photoelectric current when potential increased higher than the characteristic value for any increase in the accelerating voltage. This maximum value of the current is called as saturation current.

Effect of Frequency on Photoelectric Effect

The intensity of light is kept constant and the frequency of light is varied:

For a fixed intensity of incident light, variation in the frequency of incident light produces linear in the variation cut off potential/stopping potential of the metal. It shown cut off potential (Vc) is linearly proportional to the frequency of incident light

The kinetic energy of the photoelectrons increases directly proportionally to the frequency of incident light to completely stop the photoelectrons. We should reverse and increase the potential between the metal plate and collector in (negative value) so the emitted photoelectron can’t reach the collector.

Einstein’s Photoelectric Equation

According to Einstein’s theory on photoelectric effect is, when a photon collides inelastically with electrons, the photon is absorbed completely or partially by the electrons. So if an electron in a metal absorbs a photon of energy, it uses the energy in the following ways.

Some energy Φ0 is used to making the surface electron free from the metal. It is known as the work function of the material. Rest energy will appear as kinetic energy (K) of the emitted photoelectrons.

Einstein’s Photoelectric Equation explains the following concepts

  • The frequency of the incident light is directly proportional to the kinetic energy of the electrons and the wavelengths of incident light are inversely proportional to the kinetic energy of the electrons.
  • If γ = γth or λ =λth then vmax = 0.
  • γ < γth or λ > λth: There will be no emission of photoelectrons.
  • The intensity of the radiation or incident light refers to the number of photons in the light beam. More intensity means more photons and vice-versa. Intensity has nothing to do with the energy of the photon. Therefore, the intensity of the radiation is increased, the rate of emission increases but there will be no change in kinetic energy of electrons. With an increasing number of emitted electrons, the value of photoelectric current increases.

Different Graphs of Photoelectric Equation

  • Kinetic energy V/s frequency
  • Vmax V/s v
  • Saturated Current V/s Intensity
  • Stopping potential V/s frequency
  • Potential V/s current: (γ = constant)
  • Photoelectric current V/s Retarding potential
Important Graphs of Photoelectric Equation

Photoelectric Equation Graphs

Applications of Photoelectric Effect

  • Used to generate electricity in Solar Panels. These panels contain metal combinations that allow electricity generation from a wide range of wavelengths.
  • Motion and Position Sensors: In this case, a photoelectric material is placed in front of a UV or IR LED. When an object is placed in between the Light-emitting diode (LED) and sensor, light is cut off and the electronic circuit registers a change in potential difference
  • Lighting sensors such as the ones used in smartphones enable automatic adjustment of screen brightness according to the lighting. This is because the amount of current generated via the photoelectric effect is dependent on the intensity of light hitting the sensor.
  • Digital cameras can detect and record light because they have photoelectric sensors that respond to different colors of light.
  • X-Ray Photoelectron Spectroscopy (XPS): This technique uses x-rays to irradiate a surface and measure the kinetic energies of the emitted electrons. Important aspects of the chemistry of a surface can be obtained such as elemental composition, chemical composition, the empirical formula of compounds and chemical state.
  • Photoelectric cells are used in burglar alarms.

Problems on Photoelectric Effect

1. In a photoelectric effect experiment, the threshold wavelength of incident light is 260 nm and E (in eV) = 1237/λ (nm). Find the maximum kinetic energy of emitted electrons.

Solution:

Kmax = hc/λ – hc/λ= hc × [(λ0 – λ)/λλ0]

⇒ Kmax = (1237) × [(380 – 260)/380×260] = 1.5 eV

Therefore, the maximum kinetic energy of emitted electrons in photoelectric effect is 1.5 eV.

2. In a photoelectric experiment, the wavelength of the light incident on metal is changed from 300 nm to 400 nm and (hc/e = 1240 nm-V). Find the decrease in the stopping potential.

Solution:

hc/λ= ϕ + eV1 . . . . (i)

hcλ= ϕ + eV2 . . . . (ii)

Equation (i) – (ii)

hc(1/λ1 – 1/λ2) = e × (V1 – V2)

⇒V– V= (hc/e) × [(λ2 – λ1)/(λ1 – λ2)]

= (1240 nm V) × 100nm/(300nm × 400nm)

=12.4/12 ≈ 1V.

Therefore, the decrease in the stopping potential during the photoelectric experiment is 1V.

3. when ultraviolet light with a wavelength of 230 nm shines on a particular metal plate, electrons are emitted from plate 1, crossing the gap to plate 2 and causing a current to flow through the wire connecting the two plates The battery voltage is gradually increased until the current in the ammeter drops to zero, at which point the battery voltage is 1.30 V. 

Photoelectric Effect Solved Example

a) What is the energy of the photons in the beam of light, in eV?

b) What is the maximum kinetic energy of the emitted electrons, in eV?

Solution:

Assuming that the wavelength corresponds to the wavelength in vacuum

f=cλf = \frac{c}{\lambda }

 

f=3×1082.40×107f = \frac{3\times 10^{8}}{2.40\times 10^{-7} }

 

f = 1.25 × 1015 Hz

The energy of photon E = hf

E = (4.136 × 10-15)( 1.25 × 1015)   

note: Planck’s constant in eV s = 4.136 × 10-15 eV s

E = 5.17 eV.

b) The maximum kinetic energy related to the emitted electron is stopping potential. In this case, stopping potential is 1.30V. SO the maximum kinetic energy of the electrons is 1.30V.

 

 


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