When a metallic surface is illuminated by a light of wavelength ,… - Vidyadip

MCQ

When a metallic surface is illuminated by a light of wavelength $\lambda,$ the stopping potential for the photoelectric current is $3\, V$. When the same surface is illuminated by light of wavelength $2\, \lambda$ the stopping potential is $1\, V$. The threshold wavelength for this surface is

✓
$4 \lambda$
B
$3.5 \lambda$
C
$3 \lambda$
D
$2.75 \lambda$

✓

Answer

Correct option: A.

$4 \lambda$

a
The energy emitted is given as,

$h v=h v_{0}+K E_{\max }$

$\frac{h c}{\lambda_{\text {incident }}}=\frac{h c}{\lambda_{0}}+ eV _{ s }$

When $\lambda_{\text {incident }}=\lambda,$ then $V_{s}=3 V$

$\frac{h c}{\lambda}=\frac{h c}{\lambda_{0}}+3 eV \ldots .$ $(i)$

And for $\lambda_{\text {incident }}=2 \lambda,$ then $V_{z}=1 V$

$\frac{h c}{\lambda}=\frac{h c}{\lambda_{0}}+1 eV \ldots$ $(ii)$

On solving equations $(i)$ and $(ii)$ we get,

$\frac{2 h c}{\lambda_{0}}=\frac{1}{2} \frac{h c}{\lambda}$

$\lambda_{0}=4 \lambda$

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