If ' $E$ ' and ' $L$ ' denote the magnitude of total energy and angular momentum of revolving electron in…

If ' $E$ ' and ' $L$ ' denote the magnitude of total energy and angular momentum of revolving electron in $\mathrm{n}^{\text {th }}$ Bohr orbit, then
  1. $\mathrm{E} \propto \mathrm{L}^{-1}$
  2. $\mathrm{E} \propto \mathrm{L}$
  3. $\mathrm{E} \propto \mathrm{L}^{-2}$
  4. $\mathrm{E} \propto \mathrm{L}^2$

Solution

$\begin{aligned} & \mathrm{E} \propto \frac{1}{\mathrm{n}^2} \text { and } \mathrm{L} \propto \mathrm{n} \\ & \therefore \mathrm{E} \propto \frac{1}{\mathrm{~L}^2} \\ & \text { or } \mathrm{E} \propto \mathrm{L}^{-2}\end{aligned}$

Asked in: MHT CET 2021 (22 Sep Shift 2)

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