MHT CET · Physics · Atomic Physics
According to Bohr's theory of hydrogen atom, the total energy of the electron in the \(n^{\text {th }}\) stationary orbit is
- A directly proportional to \(\mathrm{n}\)
- B inversely proportional to \(\mathrm{n}\)
- C directly proportional to \(\mathrm{n}^2\)
- D inversely proportional to \(\mathrm{n}^2\)
Answer & Solution
Correct Answer
(D) inversely proportional to \(\mathrm{n}^2\)
Step-by-step Solution
Detailed explanation
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,
\(\begin{aligned}
& \mathrm{E}_{\mathrm{n}}=\frac{-\mathrm{mZ}^2 \mathrm{e}^4}{8 \varepsilon_0{ }^2 \mathrm{~h}^2 \mathrm{n}^2} \\
\therefore \quad & \mathrm{E}_{\mathrm{n}} \propto \frac{1}{\mathrm{n}^2}
\end{aligned}\)
\(\begin{aligned}
& \mathrm{E}_{\mathrm{n}}=\frac{-\mathrm{mZ}^2 \mathrm{e}^4}{8 \varepsilon_0{ }^2 \mathrm{~h}^2 \mathrm{n}^2} \\
\therefore \quad & \mathrm{E}_{\mathrm{n}} \propto \frac{1}{\mathrm{n}^2}
\end{aligned}\)
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