MCQ
For an electron, with $n = 3$ has only one radial node. The orbital angular momentum of the electron will be
  • A
    $0$
  • B
    $\sqrt 6 \frac{h}{{2\pi }}$
  • $\sqrt 2 \frac{h}{{2\pi }}$
  • D
    $3\left( {\frac{h}{{2\pi }}} \right)$

Answer

Correct option: C.
$\sqrt 2 \frac{h}{{2\pi }}$
c
No. of radial nodes $=n-\ell-1=1$

$3 - \ell  - 1 = 1$

$\therefore \,\ell  = 1$

Orbital angular momentum $ =\sqrt{\ell(\ell+1) \frac{\mathrm{h}}{2 \pi}} $

$=\sqrt{2} \frac{\mathrm{h}}{2 \pi}$

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