Paragraph: The key feature of Bohr's theory of spectrum of hydrogen atom is the quantization of angular…
Paragraph:
The key feature of Bohr's theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rigid. The rule to be applied is Bohr's quantization condition.Question:
In a CO molecule, the distance between $\mathrm{C}$ (mass $=12 \mathrm{amu}$ ) and $\mathrm{O}$ (mass = $16 \mathrm{amu}$ ), where $1 \mathrm{amu}=\frac{5}{3} \times 10^{-27} \mathrm{~kg}$, is close to
$2.4 \times 10^{-10} \mathrm{~m}$
$1.9 \times 10^{-10} \mathrm{~m}$
$1.3 \times 10^{-10} \mathrm{~m}$
$4.4 \times 10^{-11} \mathrm{~m}$
Solution
$I=\mu r^2$ ( where $\mu=$ reduced mass) $\mu=\frac{m_1 m_2}{m_1+m_2}=\frac{48}{7} \mathrm{amu}$ $=11.43 \times 10^{-27} \mathrm{~kg}$
Substituting in $I=\mu r^2$ we get,
$
\begin{aligned}
r & =\sqrt{\frac{I}{\mu}}=\sqrt{\frac{1.87 \times 10^{-46}}{11.43 \times 10^{-27}}} \\
& =1.28 \times 10^{-10} \mathrm{~m}
\end{aligned}
$
$\therefore$ The correct answer is (c).
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