When a metal plate is illuminated with light | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) According to Einstein's photoelectric equation: $\frac{hc}{\lambda} = W_0 + K_{max}$,where $K_{max} = \frac{1}{2}mv^2$.For $\lambda_1 = 400 \ nm =

Vedclass · Accepted Answer

$2 hc 	imes 10^6 \ J$

Vedclass · Answer

(A) According to Einstein's photoelectric equation: $\frac{hc}{\lambda} = W_0 + K_{max}$,where $K_{max} = \frac{1}{2}mv^2$.For $\lambda_1 = 400 \ nm = 400 	imes 10^{-9} \ m$ and velocity $v_1 = v$:$\frac{hc}{400 	imes 10^{-9}} = W_0 + \frac{1}{2}mv^2 \quad \dots(i)$For $\lambda_2 = 250 \ nm = 250 	imes 10^{-9} \ m$ and velocity $v_2 = 2v$:$\frac{hc}{250 	imes 10^{-9}} = W_0 + \frac{1}{2}m(2v)^2 = W_0 + 2mv^2 \quad \dots(ii)$From $(i)$,$\frac{1}{2}mv^2 = \frac{hc}{400 	imes 10^{-9}} - W_0$. Substituting this into $(ii)$:$\frac{hc}{250 	imes 10^{-9}} = W_0 + 4 \left( \frac{hc}{400 	imes 10^{-9}} - W_0 ight)$$\frac{hc}{250 	imes 10^{-9}} = W_0 + \frac{hc}{100 	imes 10^{-9}} - 4W_0$$3W_0 = hc \left( \frac{1}{100 	imes 10^{-9}} - \frac{1}{250 	imes 10^{-9}} ight)$$3W_0 = hc \left( \frac{2.5 - 1}{250 	imes 10^{-9}} ight) = hc \left( \frac{1.5}{250 	imes 10^{-9}} ight) = hc \left( \frac{15}{2500 	imes 10^{-9}} ight) = hc \left( \frac{3}{500 	imes 10^{-9}} ight)$$W_0 = \frac{hc}{500 	imes 10^{-9}} = 0.2 	imes 10^7 \ hc = 2 	imes 10^6 \ hc \ J$.

When a metal plate is illuminated with light of wavelengths $400 \ nm$ and $250 \ nm$,the maximum velocities of the emitted photoelectrons are $v$ and $2v$,respectively. The work function of the metal is ($h$ = Planck's constant; $c$ = speed of light in vacuum):

Similar Questions

When light is incident on a surface,photoelectrons are emitted. For these photoelectrons,which of the following is true?

If light of wavelength $6600 \ \mathring A$ is incident on a metal surface with a work function of $2 \ eV$,what will be the maximum kinetic energy of the emitted photoelectrons?

In the photoelectric effect, the kinetic energy of the electron emitted from the metal surface depends upon:

The maximum velocity of the photoelectron emitted by the metal surface is $v$. The charge and mass of the photoelectron are denoted by $e$ and $m$ respectively. The stopping potential in volt is

Vedclass Test Series

Exam Paper Generator

Online Exam Module