Photoelectric Effect

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Theory

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When a metal surface is illuminated with light, electrons can be emitted from the surface. This phenomenon, known as the photoelectric effect, was discovered by Heinrich Hertz in 1887 in the process of his research into electromagnetic radiation. The emitted electrons are called photoelectrons. A sample experimental arrangement for observing the photoelectric effect is illustrated in Figure 1. Light falling on a metal surface (the emitter) can release electrons, which travel to the collector. The experiment must be done in an evacuated tube, so that the electrons do not lose energy in collisions with molecules of the air. Among the properties that can be measured are the rate of electron emission and the maximum kinetic energy of the photoelectrons.

In the classical picture, the surface of the metal is illuminated by an electromagnetic wave of intensity I. The surface absorbs energy from the wave until the energy exceeds the binding energy of the electron to the metal, at which point the electron is released. The minimum quantity of energy needed to remove an electron is called the work function ϕ of the material. The minimum negative potential of the anode of a photoelectric tube for which photoelectric current stops or becomes zero is called stopping potential.

A successful theory of the photoelectric effect was developed in 1905 by Albert Einstein. Einstein proposed that the energy of electromagnetic radiation is not continuously distributed over the wave front, but instead is concentrated in localized bundles or quanta (also known as photons). The energy of a photon associated with an electromagnetic wave of frequency v is

\[E = hv = \frac{hc}{\lambda} \]

In Einstein’s interpretation, a photoelectron is released as a result of an encounter with a single photon. The entire energy of the photon is delivered instantaneously to a single photoelectron. If the photon energy hv is greater than the work function ϕ of the material, the photoelectron will be released. If the photon energy is smaller than the work function, the photoelectric effect will not occur. This explanation thus accounts for two of the failures of the wave theory: the existence of the cutoff frequency and the lack of any measurable time delay

Figure 1. Experimental setup of photoelectric effect

If the photon energy hv exceeds the work function, the excess energy appears as the kinetic energy of the electron:

\[KE_{max} = hv-\phi \]

A photon that supplies an energy equal to ϕ, exactly the minimum amount needed to remove an electron, corresponds to light of frequency equal to the cutoff frequency vc. At this frequency, there is no excess energy for kinetic energy,

\[hv_c = \phi v_c = \frac{\phi}{h} \]

The corresponding cutoff wavelength λ_c,

\[\lambda_{c} = \frac{hc}{\phi} \]

Experimental observation

1. It is an instantaneous process, i.e. as soon as light falls on the metal surface photo electrons are ejected. There is no time lag (10^-9sec)
2. For a given photosensitive material, there exist a certain minimum frequency called the cut-off or threshold frequency below which no photoelectric effect takes place.
3. Photoelectric current is directly proportional to the intensity of incident light.
4. Stopping potential value increases with increase in frequency of the incident radiation.
5. The maximum Kinetic Energy of emitted photoelectrons does not depend upon the intensity of incident light but increases linearly with increase in frequency of incident light.

Figure 2: (A) Relation between Photocurrent vs Potential (B) Maximum Photoelectron Energy as a function of frequency for ifferent metals

Table1: Work function of different materials.

Applications of Photoelectric Effect

• Photoelectric cells: Used in automatic doors, light meters, and burglar alarms to detect light.
• Solar cells: Convert sunlight directly into electricity using photoelectric principles.
• Television and camera tubes: Photocathodes emit electrons when struck by light, enabling image capture.
• Space research: Photoelectric sensors detect cosmic rays and measure light intensity from distant stars.
• Industrial applications: Used in smoke detectors, flame detectors, and process monitoring systems.