MCQ
What is the de-Broglie wavelength associated with the hydrogen electron in its third orbit
  • A
    $9.96 \times {10^{ - 10}}\,cm$
  • $9.96 \times {10^{ - 8}}\,cm$
  • C
    $9.96 \times {10^4}\,cm$
  • D
    $9.96 \times {10^8}\,cm$

Answer

Correct option: B.
$9.96 \times {10^{ - 8}}\,cm$
b
Radius of $3^{rd}$ orbit $r=R \times 3^2=9 R$

Since,

$\frac{ nh }{2 \pi}= mvr$

$\frac{ h }{ mv }=\frac{2 \pi r }{ n }$

$\lambda=\frac{ h }{ mv }=\frac{2 \pi \times 9 R }{3}$

$\lambda=6 \pi R$

We know that

$R =0.529\, \mathring A$

Therefore,

$\lambda=6 \pi \times 0.529$

$\lambda=9.96\, \mathring A$

$\lambda=9.96 \times 10^{-8} \,cm$

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