Question

According to Einstein's photoelectric equation, the graph between kinetic energy of photoelectrons ejected and the frequency of the incident radiation is:

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

According to the Einstein photoelectric equation,
$\text{K.E.}=\frac{1}{2}m{v}^2=h\nu -h{\nu }_0$
This equation is analogous to the equation of straight line, $y=mx+c$
$\therefore$ The $y-$intercept of the graph $=-h{\nu }_0$
slope $=h$
When $\text{K.E.}=0\Rightarrow h\nu -h{\nu }_0=0\Rightarrow \nu ={\nu }_0$
$\therefore x-$intercept is ${\nu }_0$.
Since the intercept is not zero, thus option (b) is incorrect and also we have a positive slope, therefore option (d) is also incorrect. Oppositely since intercept is negative, option (a) is also incorrect.
So the correction option here is (c), where ${\nu }_o$ is the threshold frequency, which means an incident light of smaller frequency than ${\nu }_o$ cannot eject electron from the metal surface.
So, the graph will be a straight line and it cuts X-axis at ${\nu }_0$.