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

Write down Einstein's photoelectric equation. When wavelength of the incident light on a metal surface is

λ_{1}

, then stopping potential is

V_{1}

and for wavelength

λ_{2}

, stopping potential is

V_{2}

. Obtain the formula for the Planck’s constant.

Accepted Answer

When a beam of light strikes the surface of the metal then the electrons will release from the surface of the electron. The energy of the photon which is required to eject the electrons is equal to threshold energy for the removal of the electron and also the kinetic energy of the electron with which the electron leaves the metal surface. The electron must have some kinetic energy when it leaves the surface of the metal if the electrons don’t have the required kinetic energy then there is no use of the ejection of electron and therefore the energy of the electron must be given such that it has threshold energy for the ejection of electron, and also it has the energy that the electrons leaves the metal surface with maximum kinetic energy.

We have, as per Einstein’s photoelectric equation: $∴ K \cdot E_{\max .} = \frac{1}{2} {mv}_{\max}^{2} . = h (v_{\circ} - v) .$

Stopping potential $\frac{(\frac{hc}{λ} - ϕ)}{e}$

$∴ V_{1} = \frac{(\frac{hc}{λ_{1}} - ϕ)}{e}$

$∴ V_{2} = \frac{(\frac{hc}{λ_{2}} - ϕ)}{e}$

$V_{1} - V_{2} = \frac{(\frac{hc}{λ_{1}} - ϕ)}{e} - \frac{(\frac{hc}{λ_{2}} - ϕ)}{e}$

$V_{1} - V_{2} = \frac{hc}{λ_{1} e} - e ϕ - \frac{hc}{λ_{2} e} + e ϕ $

$V_{1} - V_{2} = \frac{hc}{e} (\frac{1}{λ_{1}} - \frac{1}{λ_{2}})$

Write down Einstein's photoelectric equation. When wavelength of the incident light on a metal surface is $λ_{1}$ , then stopping potential is $V_{1}$ and for wavelength $λ_{2}$ , stopping potential is $V_{2}$ . Obtain the formula for the Planck’s constant.

Important Questions on Dual Nature of Radiation and Matter

Learn and Prepare for any exam you want !

Write down Einstein's photoelectric equation. When wavelength of the incident light on a metal surface is λ1 , then stopping potential is V1 and for wavelength λ2 , stopping potential is V2. Obtain the formula for the Planck’s constant.

Important Questions on Dual Nature of Radiation and Matter

Learn and Prepare for any exam you want !

Write down Einstein's photoelectric equation. When wavelength of the incident light on a metal surface is $λ_{1}$ , then stopping potential is $V_{1}$ and for wavelength $λ_{2}$ , stopping potential is $V_{2}$ . Obtain the formula for the Planck’s constant.