Dual Nature of Radiation and Matter - Result Question 28
30. For photoelectric emission from certain metal the cut-off frequency is $v$. If radiation of frequency $2 v$ impinges on the metal plate, the maximum possible velocity of the emitted electron will be ( $m$ is the electron mass)
[2013]
(a) $\sqrt{h v / m}$
(b) $\sqrt{2 h v / m}$
(c) $2 \sqrt{h v / m}$
(d) $\sqrt{h v /(2 m)}$
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Answer:
Correct Answer: 30. (b)
Solution:
- (b) From photo-electric equation,
$h v^{\prime}=h \nu+K _{\max }$ h. $2 v=h v+\frac{1}{2} mV^{2} _{\max } \quad[\therefore v^{\prime}=2 v]$
$\Rightarrow h \nu=\frac{1}{2} mV^{2} _{\max } \Rightarrow V _{\text{max }}=\sqrt{\frac{2 h \nu}{m}}$
