MHT CET · Physics · Atomic Physics
The angular momentum of the electron in the third Bohr orbit of hydrogen atom is ' \(l\) '. Its angular momentum in the fourth Bohr orbit is
- A \(4 l\)
- B \(\frac{4}{3} l\)
- C \(\frac{5}{4} l\)
- D \(\frac{3}{2} l\)
Answer & Solution
Correct Answer
(B) \(\frac{4}{3} l\)
Step-by-step Solution
Detailed explanation
Angular momentum of an electron in the nth Bohr orbit of hydrogen atom,
\(\begin{aligned}
& \mathrm{L}=\frac{\mathrm{nh}}{2 \pi} \\
& \Rightarrow \mathrm{~L} \propto \mathrm{n}
\end{aligned}\)
\(\begin{aligned} \therefore \quad \frac{\mathrm{L}_1}{\mathrm{~L}_2} & =\frac{l}{\mathrm{~L}^{\prime}}=\frac{3}{4} \\ \mathrm{~L}^{\prime} & =\frac{4}{3} l\end{aligned}\)
\(\begin{aligned}
& \mathrm{L}=\frac{\mathrm{nh}}{2 \pi} \\
& \Rightarrow \mathrm{~L} \propto \mathrm{n}
\end{aligned}\)
\(\begin{aligned} \therefore \quad \frac{\mathrm{L}_1}{\mathrm{~L}_2} & =\frac{l}{\mathrm{~L}^{\prime}}=\frac{3}{4} \\ \mathrm{~L}^{\prime} & =\frac{4}{3} l\end{aligned}\)
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