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Experimental Study of Photoelectric Effect

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Heinrich Hertz discovered the phenomena of photoelectric emission in 1887. He noticed that when the spark gap is open, it conducts electricity more easily. The ultraviolet light from the arc lamp illuminates the emitter. 

During the years 1886-1902, Hallwachs and Lenard studied photoelectric emission in depth. When ultraviolet radiation is permitted to fall on the emitter plate of an evacuated glass tube containing two electrodes, current flows through the circuit, according to Lenard. The current flow stopped as soon as the UV radiations were turned off. These findings suggest that when ultraviolet light strikes the emitter plate, electrons are expelled from it, and the electric field attracts them to the positive collecting plate. 

As a result, light falling on the emitter’s surface causes current to flow through the external circuit. Hallwachs and Lenard looked at how this photocurrent changed with collector plate potential, as well as light frequency and intensity. Certain metals, such as zinc, cadmium, and magnesium, were discovered to respond only to UV light with a short wavelength that caused electron emission from the surface. However, some alkali metals, such as lithium, sodium, potassium, cesium, and rubidium, are visible light sensitive. When these photosensitive compounds are irradiated by light, they all emit electrons. 

What is Photoelectric Effect?

The phenomenon of emission of electrons by certain substances (say metals), when exposed to radiations of suitable frequencies is called photoelectric effect and emitted electrons are called photoelectrons. 

The photoelectric effect is a one photon-one electron phenomenon. One photon cannot eject more than one photo-electron.

Experimental study of the Photoelectric effect

Heinrich Hertz discovered the phenomena of photoelectric emission in 1887. The Hertz experimental arrangement for the study of the photoelectric effect is shown in the below image.

Photoelectric Cell

It consist of,

  • Evacuated glass tube
  • Photosensitive plate (C)
  • Metal plate (A)
  • Light source (S) [Mon
  • chromatic light]
  • Quartz window (W)

Monochromatic light from the source of sufficiently short wavelength enters the tube through quartz window and falls on photosensitive plate C which acts as an emitter. The electrons are emitted by the plate C and are collected by the plate A (collector), the electric field is created by the battery. 

The potential difference applied between the plates can be changed by the potential divider arrangement. By means of commutator key the plate A can be maintained at desired positive or negative potential with respect to Plate C. 

Important Observations are,

  • When light is incident on the emitter plate the photo electrons are emitted.
  • The photo electrons are attracted by positive plate A.
  • The emission of electrons causes flow of electric current in the circuit. 
  • The potential difference between the emitter and collector plates is measured by the voltmeter (V) whereas the photoelectric current flowing in the circuit is measured by microammeter (UA).

The variation in the photoelectric effects depends upon the following factors

  • Frequency.
  • Intensity.
  • The potential difference between plates A and C.
  • The nature of the material of plate C.

Effect of frequency on photoelectric current

Collector plate A is given an appropriate positive potential. The frequency of incident light is gradually increased from its smallest value while the intensity of incident radiation remains constant. It is observed that until a specific frequency u is reached, no photoelectric current is recorded [Refer below image].

Variation of Photoelectric current with a frequency of incident radiation

This frequency is a property of emitter plate C’s material, known as the threshold frequency for that metal, and is denoted by v.

Threshold frequency

The threshold frequency is the lowest frequency of incoming radiation for which photoelectrons are merely released from photosensitive material.

The threshold frequency of emitter plate C varies depending on the material. The threshold wavelength is the wavelength that corresponds to the threshold frequency (v). If λ> λo, photoemission is not possible.

Effect of intensity of light on the photoelectric current

The collector plate A is kept at a positive potential in relation to the emitter plate C, attracting electrons emitted from C to A. The intensity of light is modified while the frequency of incident radiation and accelerating potential remains constant, and the resulting photoelectric current is monitored. Photoelectric current is observed to rise linearly with light intensity, as shown in the below image. 

Variation of photoelectric current with the intensity of light

The number of photoelectrons emitted per second is exactly proportional to the photoelectric current. This means that the rate at which photoelectrons are emitted is proportional to the intensity of incident energy.

Note: More photos, not more energetic photons, are produced by a brighter light.

Effect of potential difference on photoelectric current

The incident radiation threshold frequency and intensity are both kept constant at a reasonable value. Plate A’s positive potential is steadily increased, and the resulting photoelectric current is measured each time. It has been discovered that as the positive (accelerating potential) grows, so does the photoelectric current. All of the released electrons are captured by plate A at some point for a particular positive potential, and photoelectric current peaks. The photoelectric current does not rise as the positive potential of plate A is increased further. Saturation current refers to the highest value of photoelectric current.

The commutator key is now inverted, and plate A is given a negative (retarding) potential in relation to plate C. The negative potential of Plate A is gradually increased till the photoelectric current reduces to zero. The minimum negative potential V_{0} given to the plate A for which photoelectric current stops or becomes zero is called cut-off or stopping potential.

Variation of photoelectric current with collector plate potential for different intensities of incident radiation

The energy of all photoelectrons released from a metal surface is not the same. When the stopping potential is adequate to reject even the most energetic photoelectrons with the highest kinetic energy, the photoelectric current becomes zero, and 

1 / 2 mv2max = eV0.

where 

vmax is the maximum velocity of the photoelectron,

m is the mass of the electron, and

e is the magnitude of the charge on the electron.

When the incident radiation frequency is maintained constant and the experiment is repeated with varying strengths of the incident beam, it is discovered that V remains constant in all circumstances see above image. The stopping potential and maximum kinetic energy of photoelectrons are thus independent of incoming radiation intensity for a certain frequency of incident radiation.

Variation of photoelectric current with collector plate potential for different frequencies of incident radiation

Adjusting the same intensity of incoming radiation at various frequencies to study the fluctuation of photoelectric current with collector plate potential is illustrated in the figure. For incoming radiation of various frequencies, different values of stopping potential but the same values of saturation current are achieved. The energy of a photoelectron released is proportional to the frequency of incoming light. When the frequency of incoming radiation is increased, the stopping potential becomes more negative.

As shown, the below graph between incoming radiation frequency and related stopping potential for various metals is made up of straight lines.

Variation of stopping potential with the frequency of incident radiations

The graph shows that, for a particular photosensitive material, the stopping potential varies linearly with the frequency of incoming radiation, and there is a minimum cut-off frequency v0 below which the stopping potential is zero.

Sample Questions

Question 1: Define threshold frequency and photoelectric work function?

Answer: 

Threshold frequency: The threshold frequency is the lowest frequency of incoming radiation for which photoelectrons are merely released from photosensitive material.

Photoelectric work function: The photoelectric work function is the threshold energy required by the radiation or photons that are incident on the surface of the metal. We can use the term radiation interchangeably with photons in this case. 

ϕ=hν0 

where h is the Planck’s constant and ν0 is the threshold frequency.

Question 2: What is the photoelectric effect? State and explain its characteristics?

Answer: 

The phenomenon of emission of electrons by certain substances (say metals), when exposed to radiations of suitable frequencies is called photoelectric effect and emitted electrons are called photoelectrons. The photoelectric effect is a one photon-one electron phenomenon. One photon cannot eject more than one photo-electron.

Characteristics: 

  • For a given photosensitive material, there exists a certain minimum cut-off frequency of the incident radiation, called threshold frequency v0 below which no emission of photoelectrons takes place. The threshold frequency is different for different metals.
  • For a given photosensitive material and frequency of incident radiation (above threshold frequency), the photoelectric current is directly proportional to the intensity of incident light.
  • Above the threshold frequency v0, the maximum kinetic energy of the emitted photoelectrons increases linearly with the frequency of the incident radiation, but is independent of intensity of incident radiation.
  •  The emission of photo electron is an instantaneous process. There is no time lag between the irradiation of the metal surface and P emission of photoelectrons.

Question 3: Define threshold wavelength?

Answer: 

The wavelength (λ0) corresponding to the threshold frequency v0, is called the threshold wavelength. 

If c is the velocity of light, then

v0 = ϕ / h

For the photoelectric emission the wavelength of incident light must be less than λ0. 

Question 4: What is the mass of a photon?

Answer:

The photon’s rest mass is zero, which indicates that if the photon is moving, it will have some momentum, which is equivalent to mass, but at rest, the photon’s mass will be zero.

Question 5: Define stopping potential?

Answer: 

The magnitude of the retarding potential for which the photoelectric current is zero is called the stopping potential (Vs)

The value of the stopping potential is a measure of the maximum kinetic energy for the photoelectrons.

Work done on electron by,

Vs = Max K.E. for the photoelectrons.

eVs = 1/2 mv2max

Question 6: What is the effect of kinetic energies on stopping potential in photoelectric emission?

Answer: 

The value of the stopping potential is a measure of the maximum kinetic energy that can be possessed by a photoelectron. 

The different photoelectrons have different kinetic energies. At the stopping potential, the work done by the electron against the stopping potential V is equal to the K.E. of this electron having maximum K.E.

eV = 1/2 mv2max

where V max is the maximum velocity.


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Last Updated : 28 Apr, 2022
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