A certain metallic surface is illuminated with monochromatic ligh… - Vidyadip

MCQ

A certain metallic surface is illuminated with monochromatic light of wavelength, $\lambda$. The stopping potential for photo-electric current for this light is $3 V_0$ . If the same surface is illuminated with light of wavelength $2\lambda$, the stopping potential is $V_0$. The threshold wavelength for this surface for photo- electric effect is

A
$6\lambda$
✓
$4\lambda$
C
$\frac{\lambda }{4}$
D
$\frac{\lambda }{6}$

✓

Answer

Correct option: B.

$4\lambda$

b
Case $(i)$, $e 3 V_{0}=\frac{h c}{\lambda}-\phi_{0}$ ......... $(i)$

Case $(ii)$, $e V_{0}=\frac{h c}{2 \lambda}-\phi_{0}$ .........$(ii)$

From $(i)$ and $(ii)$ we get,

$\frac{3 h c}{2 \lambda}-3 \phi_{0}=\frac{h c}{\lambda}-\phi_{0}$

or $\frac{3 h \lambda}{2 \lambda}-\frac{h c}{\lambda}=3 \phi_{0}-\phi_{0}$

or $\frac{h c}{2 \lambda}=2 \phi_{0}$ or $\phi_{0}=\frac{h c}{4 \lambda}$

$\therefore $ Threshold wavelength

$\lambda_{0}=\frac{h c}{\phi_{0}}=\frac{h c}{h c} \times 4 \lambda=4 \lambda$

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