Name: Photoelectric Effect: Threshold Frequency & Wavelength
Uploaded: 2019-07-19
Duration: 5 min 56 s
Description: This video sheds light on the concepts of threshold frequency, threshold wavelength of metal, and their relation with the work function. Watch the video to l...

Question

Derive Einstein's Photoelectric equation. Explain photoelectric effect with help of this equation.

Accepted Answer

Einstein's photoelectric equation.
According to Einstein, the emission of photoelectron is the result of the interaction between a single photon of the incident radiation and an electron in the metal.
When a photon of energy hv is incident on a metal surface, its energy is used up in two ways.
(i) A part of the energy of the photon is used in extracting the electron from the surface of metal, since the electrons in the metal are bound to the nucleus. This energy W spent in releasing the photoelectron is known as photoelectric work function of the metal. The work function of a photo metal is defined as the minimum amount of energy required to liberate an electron from the metal surface.
(ii) The remaining energy of the photon is used to impart kinetic energy to the liberated electron. If m is the mass of an electron and v its velocity, then
Energy of the incident photon = Work function + Kinetic energy of the electron

$h ν = W + \frac{1}{2} m v^{2}$ ...........(1)

If the electron does not lose energy by internal collisions, as it escapes from the metal, the entire energy (h−W) will be exhibited as the kinetic energy of the electron Thus, (h−W) represents the maximum kinetic energy of the ejected photoelectron. If $V_{m a x}$ is the maximum velocity with which the photoelectron can be ejected, then

$h v = W + \frac{1}{2} m {v^{2}}_{m a x}$ .............(2)

This equation is known as Einstein's photoelectric equation.

When the frequency( $γ$ ) of the incident radiation is equal to the threshold frequency ( $γ_{0}$ )of the metal surface, kinetic energy of the electron is zero. Then equation (2) becomes,

$h γ_{0} = W$ ............(3)

Substituting the value of W in equation (2) we get,

$h γ - h γ_{0} = m {v^{2}}_{m a x} o r h (γ - γ_{0}) = m {v^{2}}_{m a x}$

This is another form of Einstein's photoelectric equation.

Derive Einstein's Photoelectric equation. Explain photoelectric effect with help of this equation.

Important Questions on Dual Nature of Radiation and Matter

Learn and Prepare for any exam you want !