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

MCQ

When a metallic surface is illuminated with light of wavelength $\lambda$, the stopping potential is $x$ volt. When the same surface is illuminated by light of wavelength $2 \lambda$, the stopping potential is $\frac{x}{3}$. Threshold wavelength for the metallic surface is ..........

A
$\frac{4 \lambda}{3}$
✓
$4 \lambda$
C
$6 \lambda$
D
$\frac{8 \lambda}{3}$

✓

Answer

Correct option: B.

$4 \lambda$

b
(b)

From Einstein photoelectric equation.

$h . v=\phi+ K _{\max }$

$\frac{h c}{\lambda}=\phi+e v_0$ $\quad \left(v_6=\right.$ stopping potential)

$\frac{h c}{\lambda}=\phi+e x$

$\frac{h c}{2 \lambda}=\phi+e \frac{x}{3}$

On solving

(work function) $\phi=\frac{h c}{4 \lambda}$

$\frac{h c}{\lambda_0}=\frac{h c}{4 \lambda}$

$\lambda_0=4 \lambda$

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