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

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 11. Dual nature of radiation and matter4 Marks
MCQ
Electron beam used in an electron microscope, when accelerated by a voltage of $20\,kV$. has a de-Broglie wavelength of $\lambda_0$. If the voltage is increased to $40\,kV$. then the de-Broglie wavelength associated with the electron beam would be:
  • A
    $3 \lambda_0$
  • B
    $9 \lambda_0$
  • C
    $\frac{\lambda_0}{2}$
  • ✓
    $\frac{\lambda_0}{\sqrt{2}}$
✓

Answer

Correct option: D.
$\frac{\lambda_0}{\sqrt{2}}$
d
When electron is accelerated through potential difference $V$, then

$\text { K.E. }= eV$

$\Rightarrow \lambda=\frac{ h }{\sqrt{2 m ( KE )}}=\frac{ h }{\sqrt{2 meV }}$

$\therefore \quad \lambda \propto \frac{1}{\sqrt{ V }}$

$\therefore \quad \frac{\lambda}{\lambda_0}=\sqrt{\frac{20}{40}}$

$\therefore \quad \lambda=\frac{\lambda_0}{\sqrt{2}}$

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