Photoelectric Effect Formula

A photon particle is the tiny blob of pure energy. In the photoelectric effect, the electron is attacked by a wandering blob of energy. Hence electron gets excited and further, it breaks its bond with the atom to which it is held. Under suitable circumstances, we can use light to push electrons and free them from the surface of a solid. This process is termed as the photoelectric effect or photoelectric emission. This article will explain this phenomenon with a suitable photoelectric effect formula and examples. Let us learn the interesting concept!

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What is the Photoelectric Effect?

This interesting effect was first observed in 1887 by scientist Heinrich Hertz during his experiments with a spark gap generator. In it sparks generated between two small metal spheres in a transmitter induce sparks. Then they jump between two different metal spheres in the receiver. Thus, it is the process that involves the release of electrons from the surface of metal materials when light falls on them. This concept enables us to clearly understand the quantum nature of light and electrons.

After continuous research in this field, Albert Einstein gave its successful explanation. He concluded that it was occurring due to the result of light energy being carried in discrete quantized packets.

Source: en.wikipedia.org

The Formula for Photoelectric Effect

According to the famous Einstein explanation of the photoelectric effect: The energy of the photon will be sum total of energy needed to remove the electron and kinetic energy of the emitted electron.

Thus \(h \nu= W + E\)

Where,

h	Planck’s constant.
\(\nu\)	Frequency of the incident photon.
W	Work function.
E	The maximum possible kinetic energy of the emitted electron. It will be \(\frac{1}{2} mv^{2}\), for mass m and velocity v of the electron.

Laws of Photoelectric Effect:

1. For a light of frequency; \(\gamma > \gamma_{th}\), photoelectric current is proportional to the intensity of light.
2. For any given material, there is some minimum-energy frequency, which is the threshold frequency. Below is the emission of photoelectrons stops completely, irrespective of the intensity of incident light.
3. The maximum kinetic energy of the photoelectrons increases with the increase in the frequency of incident light. The maximum kinetic energy is not dependent on the intensity of light.
4. The photo-emission is the instantaneous process.

Solved Examples for Photoelectric Effect Formula

Q.1: What are some applications of the Photoelectric Effect?

Solution: Some applications are as follows:

• Used to generate electricity in Solar Panels.
• Used in motion and Position Sensors.
• For lighting sensors such as the ones used in smartphone enable automatic adjustment of screen brightness
• In X-Ray Photoelectron Spectroscopy i.e. XPS.
• Digital cameras are able to detect and record the light due to having photoelectric sensors.

Q.2: Monochromatic light of wavelength 400 nm strikes a plate of metal. This metal has a work function of 2.14 eV. Use Photoelectric Effect Formula to find the energy of the electrons that eject.

Solution: Given here,

Planck’s constant,\( h = 6.62 \times 10^{-34} Js\)

Wavelength, \(\lambda= 400 nm = 400 \times 10^{-9} m\)

Thus frequency, \(\nu = \frac{1}{ 400 \times 10^{-9}} = 2.5 \times 10^{6} Hz.\)

The energy equation is: \(E = h \nu – W\)

\(= 6.62 \times 10^{-34} \times 2.5 \times 10^{6} – 2.4 eV\\\)

\(= -3.4 \times 10^{-19} J = -2.12 eV\)

Since work function is greater in magnitude than the energy obtained, so there will be no current generated.