Question:
If the de Broglie wavelength of the electron in $\mathrm{n}^{\text {th }}$ Bohr orbit in a hydrogenic atom is equal to $1.5 \pi \mathrm{a}_{0}\left(\mathrm{a}_{0}\right.$ is Bohr radius), then the value of $\mathrm{n} / \mathrm{z}$ is :
Correct Option: , 4
Solution:
Given $\lambda=1.5 \pi a_{0}$
$n \lambda=2 \pi r$ ...(i)
Radii of stationary states $(r)$ is expressed as:
$r=a_{0} \frac{n^{2}}{z}$ ...(ii)
From eqn (i) and (ii)
$n \lambda=\frac{2 \pi a_{0} n^{2}}{z} ; \lambda=\frac{2 \pi a_{0} n}{z}$
$1.5 \pi a_{0}=2 \pi a_{0} \frac{n}{z}$
$\frac{n}{z}=\frac{3}{4}=0.75$
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