MCQ
If the de Brogile wavelength of the electron in $n^{th}$ Bohr orbit in a hydrogenic atom is equal to $1.5\,\pi a_0$ ( $a_0$ is Bohr radius), then the value of $n/z$ is
  • A
    $0.40$
  • B
    $1.50$
  • C
    $1.0$
  • $0.75$

Answer

Correct option: D.
$0.75$
d
$2\pi r = n\lambda $

$\lambda  = \frac{{2\pi r}}{n} = \frac{{2\pi {n^2}{a_0}}}{{n \times Z}} = 2\pi \frac{n}{Z}{a_0}$

$\lambda  = 1.5\pi {a_0}$

$\therefore \,2\pi \frac{n}{Z}{a_0} = 1.5\pi {a_0}$

$\therefore \frac{n}{Z} = \frac{{1.5}}{2} = 0.75$

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