MCQ
If the radius of first orbit of $H$ atom is $a_0$, the de-Broglie wavelength of an electron in the third orbit is
  • A
    $4\pi {a_0}$
  • B
    $8\pi {a_0}$
  • $6\pi {a_0}$
  • D
    $2\pi {a_0}$

Answer

Correct option: C.
$6\pi {a_0}$
c
${r_H} = {a_0}{n^2}$

$r = {a_0} \times {(3)^2} = 9{a_0}$

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

$mv = \frac{{nh}}{{2\pi r}} = \frac{{3h}}{{2\pi  \times 9{a_0}}} = \frac{h}{{6\pi \,{a_0}}}$

$\lambda  = \frac{h}{{mv}} = \frac{h}{h} \times 6\pi {a_0} = 6\pi {a_0}$

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