Question

The maximum velocity of electrons emitted from a metal surface is $v$ when the frequency of light falling on it is $f$ . The maximum velocity when the frequency becomes $4f$ is

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

Answer 1

Answer: (B)

According to Einstein's equation for P.E.E.
For $1^{s t}$ case,
$\frac{1}{2}mv^{2}=hf-W$ , where $f=$ frequency of incident light and $W=$ work function
For $2^{n d}$ case,
$\frac{1}{2}\left(\left(mv\right)_{1}\right)^{2}=h\left(4 f\right)-W$
$\frac{1}{2}mv_{1}^{2}=4hf-4W+3W$
$\frac{1}{2}\left(\left(mv\right)_{1}\right)^{2}=4\left(hf - W\right)+3W$
$\frac{1}{2}mv_{1}^{2}=4\frac{1}{2}mv^{2}+3W$
$\frac{1}{2}\left(mv\right)_{1}\right)^{2}=\frac{1}{2}m\left(2 v\right)^{2}+3W$
This equation tells us on comparison that,
$v_{1}>2v$