Modern Physics Ques 37
Passage Based Questions
Passage
The key feature of Bohr’s theory of spectrum of hydrogen atom is the quantisation of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantised rotational energy of a diatomic molecule assuming it to be rigid. The rule to be applied is Bohr’s quantisation condition.
- A diatomic molecule has moment of inertia $I$. By Bohr’s quantization condition its rotational energy in the $n$th level ( $n=0$ is not allowed) is
(2010)
(a) $\frac{1}{n^{2}} (\frac{h^{2}}{8 \pi^{2} I})$
(b) $\frac{1}{n} (\frac{h^{2}}{8 \pi^{2} I})$
(c) $n (\frac{h^{2}}{8 \pi^{2} I})$
(d) $n^{2} (\frac{h^{2}}{8 \pi^{2} I})$
Show Answer
Answer:
Correct Answer: 37.(d)
Solution:
Formula:
- $L=I \omega=\frac{n h}{2 \pi}$
$\therefore \quad \omega=\frac{n h}{2 \pi I}$
$ K=\frac{1}{2} I \omega^{2}=\frac{1}{2} I (\frac{n h}{2 \pi I}){ }^{2}=\frac{n^{2} h^{2}}{8 \pi^{2} I} $
BETA
