MHT CET · Physics · Atomic Physics
In hydrogen atom, if \(V_n\) and \(V_p\) are orbital velocities in \(\mathrm{n}^{\text {th }}\) and \(\mathrm{p}^{\text {th }}\) orbit respectively, then the ratio \(V_p: V_n\) is
- A \(\mathrm{p}: \mathrm{n}\)
- B \(\mathrm{n}: \mathrm{p}\)
- C \(\mathrm{p}^2: \mathrm{n}^2\)
- D \(\mathrm{n}^2: \mathrm{p}^2\)
Answer & Solution
Correct Answer
(B) \(\mathrm{n}: \mathrm{p}\)
Step-by-step Solution
Detailed explanation
Velocity of electron in \(n^{\text {th }}\) orbit of hydrogen atom, \(\mathrm{V}_{\mathrm{n}}=\frac{\mathrm{e}^2}{2 \varepsilon_0 \mathrm{hn}}\)
\(\begin{array}{ll}
\therefore & \mathrm{V}_{\mathrm{n}} \propto \frac{1}{\mathrm{n}} \\
\therefore & \frac{\mathrm{~V}_{\mathrm{p}}}{\mathrm{~V}_{\mathrm{n}}}=\frac{\mathrm{n}}{\mathrm{p}}
\end{array}\)
\(\begin{array}{ll}
\therefore & \mathrm{V}_{\mathrm{n}} \propto \frac{1}{\mathrm{n}} \\
\therefore & \frac{\mathrm{~V}_{\mathrm{p}}}{\mathrm{~V}_{\mathrm{n}}}=\frac{\mathrm{n}}{\mathrm{p}}
\end{array}\)
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