Question: Q. 2. Using Bohr’s postulates, derive the expression for the orbital period of the electron moving in the $\mathrm{n}^{\text {th }}$ orbit of hydrogen atom.
R [Foreign, I, II, III 2017]
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Solution:
Ans.
$$ m v r=\frac{n h}{2 \pi} \quad \ldots . \text { Bohr postulate } 1 / 2 $$
Also,
$$ \frac{m v^{2}}{r}=\frac{1}{4 \pi \varepsilon_{0}} \frac{e^{2}}{r^{2}} $$
$$ \begin{aligned} \Rightarrow \quad m v^{2} r & =\frac{e^{2}}{4 \pi \varepsilon_{0}} \ \Rightarrow \quad v & =\frac{e^{2}}{4 \pi \varepsilon_{0}} \times \frac{2 \pi}{n h}=\frac{e^{2}}{2 \varepsilon_{0} n h} \end{aligned} $$
$1 / 2$
(Also accept if the student calculates $T$ by obtaining expressions for both $v$ and $r$.)
[CBSE Marking Scheme 2017]
