Modern Physics 2 Question 21
20. For photo-electric effect with incident photon wavelength $\lambda$, the stopping potential is $V _0$. Identify the correct variation(s) of $V _0$ with $\lambda$ and $\frac{1}{\lambda}$.
(2015 Adv.) (a)
(c)
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Solution:
$$ \begin{aligned} e V _0 & =\frac{h c}{\lambda}-W \\ V _0 & =\frac{h c}{e} \frac{1}{\lambda}-\frac{W}{e} \end{aligned} $$
$V _0$ versus $\frac{1}{\lambda}$ graph is in the form $y=m x-c$
Therefore option (c) is correct.
Clearly, $V _0$ versus $\lambda$ graph is not a straight line but $V _0$ decreases with increase in $\lambda$ and $V _0$ becomes zero when $\frac{h c}{\lambda}=W$.
$$ \text { i.e. } $$
$\lambda=\lambda _0$
(Threshold wavelength)
$\therefore$ Option (a) is also correct.
