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JEE Main 20245 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
5 April
Shift
Evening Shift
Subject
Physics
Chapter
Atomic Physics

JEE Main 2024 · 5 April · Evening Shift · Physics · Atomic Physics

The angular momentum of an electron in a hydrogen atom is...

The angular momentum of an electron in a hydrogen atom is proportional to : (Where rr is the radius of orbit of electron)

Options

  1. Ar
  2. Br\sqrt{\mathrm{r}}
  3. C1r\frac{1}{\sqrt{\mathrm{r}}}
  4. D1r\frac{1}{\mathrm{r}}

Correct answer

B. r\sqrt{\mathrm{r}}

Step-by-step solution

FC=mv2rKq1q2r2=mv2rmv2r2=K K1q2rL2 m=KKq1q2rL∝r\begin{aligned} & \mathrm{F}_{\mathrm{C}}=\frac{\mathrm{mv}^2}{\mathrm{r}} \\ & \frac{\mathrm{Kq}_1 \mathrm{q}_2}{\mathrm{r}^2}=\frac{\mathrm{mv}^2}{\mathrm{r}} \\ & \mathrm{mv}^2 \mathrm{r}^2=K \mathrm{~K}_1 \mathrm{q}_2 \mathrm{r} \\ & \frac{\mathrm{L}^2}{\mathrm{~m}}=K \mathrm{Kq}_1 \mathrm{q}_2 \mathrm{r} \\ & \mathrm{L} \propto \sqrt{\mathrm{r}}\end{aligned}
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