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12. atoms — Physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 SciencePhysics12. atoms1 Mark
MCQ
With what potential an electron should be accelerated so that its de Broglie wavelength becomes equal to the wavelength of first line of lymen series for $He^+$ ion ?
  • A
    $\frac{{{R^2}{h^2}}}{{2me}}$
  • ✓
    $\frac{{{9R^2}{h^2}}}{{2me}}$
  • C
    $\frac{{{9R^2}{h^2}}}{{32me}}$
  • D
    $\frac{{{R^2}{h^2}}}{{32me}}$
✓

Answer

Correct option: B.
$\frac{{{9R^2}{h^2}}}{{2me}}$
b
$\frac{\mathrm{h}}{\sqrt{2 \mathrm{meV}}}=\frac{1}{\mathrm{R}(2)^{2}\left(\frac{1}{1^{2}}-\frac{1}{2^{2}}\right)}$

$\Rightarrow \frac{\mathrm{h}}{\sqrt{2 \mathrm{meV}}}=\frac{1}{4 \mathrm{R}\left(\frac{3}{4}\right)}=\frac{1}{3 \mathrm{R}}$

$\frac{\mathrm{h}^{2}}{2 \mathrm{meV}}=\frac{1}{9 \mathrm{R}^{2}} \Rightarrow \mathrm{V}=\frac{9 \mathrm{R}^{2} \mathrm{h}^{2}}{2 \mathrm{me}}$

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