Question

The maximum velocity of electrons emitted from a metal surface is $v$. What would be the maximum velocity if frequency of the light is increased by a factor of 4?

• A. 2$v$
• B. > 2$v$
• C. < 2$v$
• D. between 2$v$ and 4$v$

Answer 1

The correct option is B > 2$v$

$\frac{1}{2}m{v}^2=hf-{\varphi }_0$$\frac{1}{2}m{v}^{\text{'}2}=4hf-{\varphi }_0$
$\frac{v^{\text{'}2}}{v^2}=\frac{4hf-{\varphi }_0}{hf-{\varphi }_0}$
$\frac{v^{\text{'}2}}{v^2}=\frac{4[hf-{\varphi }_0]+3{\varphi }_0}{hf-{\varphi }_0}$
Clearly, $v^{\prime }>2v$