# If the de Broglie wavelength of the electron in

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 :

1. $0.40$

2. $1.50$

3. $1.0$

4. $0.75$

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)

$n \lambda=\frac{2 \pi a_{0} n^{2}}{z} ; \lambda=\frac{2 \pi a_{0} n}{z}$

$1.5 \pi a_{0}=2 \pi a_{0} \frac{n}{z}$

$\frac{n}{z}=\frac{3}{4}=0.75$