The surface of a metal is illuminated alternately with photons of energies $E_{1} = 4 eV$ and $E_{2} = 2.5 eV$ respectilvely. The ratio of maximum speeds of the photoelectrons emitted in two cases is $2$ . The work function of metal in $(eV)$ is

Open in App

Solution

From the Einstein's photoelectric equation,

$\Rightarrow$ Kinetic energy = Energy of Photon - Work Function
Let $ϕ_{0}$ be the work function or metal and $v_{1}$ and $v_{2}$ be the velocity of photoelectrons. Using Einsteins photoelectric equation we have
$\frac{1}{2} m v_{1}^{2} = 4 - ϕ_{0} . . . . (i)$
$\frac{1}{2} m v_{2}^{2} = 2.5 - ϕ_{0} . . . . (i i)$
$\Rightarrow \frac{\frac{1}{2} m v_{1}^{2}}{\frac{1}{2} m v_{2}^{2}} = \frac{4 - ϕ_{0}}{2.5 - ϕ_{0}}$
$\Rightarrow (2)^{2} = \frac{4 - ϕ_{0}}{2.5 - ϕ_{0}} \Rightarrow 10 - 4 ϕ_{0} = 4 - ϕ_{0}$
$\Rightarrow ϕ_{0} = 2 eV$

Suggest Corrections

Similar questions

Q. Two photons of energy

2.5 e V

and

3.5 e V

fall on a metal surface of work function

1.5 e V

. The ratio of the maximum velocities of the photoelectrons emitted from the metal surface is:

Q. Light of two different frequencies whose photons have energies

1 e V

and

2.5 e V

respectively, successively illuminate a metallic surface whose work function is

0.5 e V

. Ratio of maximum speeds of emitted electrons will be :

Light of two different frequencies whose photons have energies 1 eV and 2.5 eV respectively, successively illuminate a metallic surface whose work function is 0.5 eV. Ratio of maximum speeds of emitted electrons will be

Q. Photons of energies 1 eV and 2.5 eV are incident on a metal surface of work function 0.5 eV. Then the ratio of maximum velocities with which the photoelectrons are emitted being

Q. Photons of energy

1

eV and

2.5

eV successively illuminate a metal whose work function if

0.5

eV. The ratio of maximum speed of emitted electrons is ________.

Join BYJU'S Learning Program

The surface of a metal is illuminated alternately with photons of energies E1=4 eV and E2=2.5 eV respectilvely. The ratio of maximum speeds of the photoelectrons emitted in two cases is 2. The work function of metal in (eV) is

The surface of a metal is illuminated alternately with photons of energies $E_{1} = 4 eV$ and $E_{2} = 2.5 eV$ respectilvely. The ratio of maximum speeds of the photoelectrons emitted in two cases is $2$ . The work function of metal in $(eV)$ is