According to Bohr's theory of hydrogen atom, the total energy of the electron in the $n^{\text {th }}$…

According to Bohr's theory of hydrogen atom, the total energy of the electron in the $n^{\text {th }}$ stationary orbit is
  1. directly proportional to $\mathrm{n}$
  2. inversely proportional to $\mathrm{n}$
  3. directly proportional to $\mathrm{n}^2$
  4. inversely proportional to $\mathrm{n}^2$

Solution

According to Bohr's theory of hydrogen atom, the equation for total energy of the electron in the $\mathrm{n}^{\mathrm{th}}$ stationary orbit is, $\begin{aligned} & \mathrm{E}_{\mathrm{n}}=\frac{-\mathrm{mZ}^2 \mathrm{e}^4}{8 \varepsilon_0{ }^2 \mathrm{~h}^2 \mathrm{n}^2} \\ \therefore \quad & \mathrm{E}_{\mathrm{n}} \propto \frac{1}{\mathrm{n}^2} \end{aligned}$ ^

Asked in: MHT CET 2023 (11 May Shift 2)

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