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

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 12 - 11. Dual nature of radiation and matter4 Marks
Question
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
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Answer

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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