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11. Dual nature of radiation and matter — Physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 SciencePhysics11. Dual nature of radiation and matter1 Mark
MCQ
When a metallic surface is illuminated with radiation of wavelength $\lambda$ , the stopping potential is $V.$ If the same surface is illuminated with radiation of wavelength $2\lambda$, the stopping potential is $\frac{V}{4}$. The threshold wavelength for the metallic surface is 
  • A
    $5\lambda$
  • B
    $\frac{5}{2}\lambda $
  • ✓
    $3\lambda$
  • D
    $4\lambda$
✓

Answer

Correct option: C.
$3\lambda$
c
According to Einstein's photoelectric equation,

$e V_{s}=\frac{h c}{\lambda}-\frac{h c}{\lambda_{0}}$

$\therefore$ As per question, $e V=\frac{h c}{\lambda}-\frac{h c}{\lambda_{0}}$   ..... $(i)$

$\frac{e V}{4}=\frac{h c}{2 \lambda}-\frac{h c}{\lambda_{0}}$   ..... $(ii)$

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

$\frac{h c}{2 \lambda}-\frac{h c}{4 \lambda}=\frac{h c}{\lambda_{0}}-\frac{h c}{4 \lambda_{0}}$

$\Rightarrow \frac{h c}{4 \lambda}=\frac{3 h c}{4 \lambda_{0}}$ or $\lambda_{0}=3 \lambda$

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