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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
Light of wavelength $\lambda$ strikes a photoelectric surface and electrons are ejected with kinetic energy $K$. If $K$ is to be increased to twice its original value, the wavelength must be changed to $\lambda'$ such that :-
  • A
    $\lambda' < \lambda/2$
  • B
    $\lambda' > \lambda/2$
  • ✓
    $\lambda > \lambda' > \lambda/2$
  • D
    $\lambda' = \lambda/2$
✓

Answer

Correct option: C.
$\lambda > \lambda' > \lambda/2$
c
$\frac{\mathrm{hc}}{\lambda^{\prime}}=2 \varepsilon+\phi$

$\frac{\mathrm{hc}}{\lambda}=\varepsilon+\phi$

Dividing them, $\frac{\lambda^{\prime}}{\lambda}=\frac{\varepsilon+\phi}{2 \varepsilon+\phi}$

or $\frac{{{\lambda ^\prime }}}{\lambda } < 1,$ so ${\lambda ^\prime } < \lambda $

Also, $\frac{{\lambda '}}{\lambda } = \frac{1}{2}\left[ {\frac{{\varepsilon  + \phi }}{{\varepsilon  + \frac{\phi }{2}}}} \right]$

$\frac{{\lambda '}}{\lambda } > \frac{1}{2}$ or $\lambda  > {\lambda ^\prime } > \lambda /2$

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