Question 194: Dual Nature of Matter and Radiation

Question

The maximum velocity of the photoelectrons emitted from the surface is v when light of frequency n falls on a metal surface. If the incident frequency is increased to 3n, the maximum velocity of the ejected photoelectrons will be :

Accepted Answer

The given maximum velocity is v and frequency is n. We know that the kinetic energy is given by
$$KE = {1 \over 2}m{v^2} = hn - \phi $$
where h is Planck's constant and $$\phi$$ is the work function. Therefore, the kinetic energy of the incident light is
$${E_1} = hn - \phi $$ ..... (1)
When the frequency of the incident light is increased to 3n, then the kinetic energy is given by
$${1 \over 2}mv_1^2 = 3hn - \phi $$
$$ \Rightarrow {E_2} = 3hn - \phi $$ ..... (2)
Substituting $$hn = {E_1} + \phi $$ [from Eq. (1)] in Eq. (2), we get
$${E_2} = 3({E_1} + \phi ) - \phi $$
$$ \Rightarrow {E_2} = 3{E_1} + 2\phi $$
$$ \Rightarrow {1 \over 2}mv_1^2 = 3 	imes {1 \over 2}m{v^2} + 2\phi $$
$$ \Rightarrow v_1^2 = 3{v^2} + 2\phi  	imes {2 \over m}$$
$$ \Rightarrow v_1^2 = 3{v^2} + {{4\phi } \over m}$$
Thus, the velocity is more than $$\sqrt 3 v$$.

Answer

less than $$\sqrt 3 $$ v

Answer

v

Answer

more than $$\sqrt 3 \,v$$

Answer

equal to  $$\sqrt 3 \,v$$

Dual Nature of Matter and Radiation

The maximum velocity of the photoelectrons emitted from the surface is v when light of frequency n falls on a metal surface. If the incident frequency is increased to 3n, the maximum velocity of the ejected photoelectrons will be :

Choose the correct answer: