MHT CET · Physics · Atomic Physics
Which of the following statements about the Bohr model of the hydrogen atom is false?
- A Acceleration of electron in \(\mathrm{n}=2\) orbit is less than that in \(n=1\) orbit.
- B Angular momentum of electron in \(\mathrm{n}=2\) orbit is more than that in \(\mathrm{n}=1\) orbit.
- C Kinetic energy of electron in \(\mathrm{n}=2\) orbit is less than that in \(\mathrm{n}=1\) orbit.
- D Potential energy of electron in \(\mathrm{n}=2\) orbit is less than that in \(\mathrm{n}=1\) orbit.
Answer & Solution
Correct Answer
(D) Potential energy of electron in \(\mathrm{n}=2\) orbit is less than that in \(\mathrm{n}=1\) orbit.
Step-by-step Solution
Detailed explanation
Potential energy in \(\mathrm{n}^{\text {th }}\) orbit is given by,
\(\begin{array}{ll}
\therefore & P . E=-\frac{m_e Z^2 e^4}{4 \varepsilon_0{ }^2 \mathrm{n}^2 h^2} \\
\therefore & P . E \propto \frac{1}{\mathrm{n}^2}
\end{array}\)
\(\begin{array}{ll}
\therefore & P . E=-\frac{m_e Z^2 e^4}{4 \varepsilon_0{ }^2 \mathrm{n}^2 h^2} \\
\therefore & P . E \propto \frac{1}{\mathrm{n}^2}
\end{array}\)
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