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. $1.0$

  2. $0.75$

  3. $0.40$

  4. $1.50$

Correct Option: 2

Solution:

According to de-broglie's hypothesis

$2 \pi \mathrm{r}_{\mathrm{n}}=\mathrm{n} \lambda \Rightarrow 2 \pi \cdot \mathrm{a}_{0}=\frac{\mathrm{n}^{2}}{\mathrm{z}}=\mathrm{n} \times 1.5 \pi \mathrm{a}_{0}$

$\frac{\mathrm{n}}{\mathrm{z}}=0.75$

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