In hydrogen atom, if $V_n$ and $V_p$ are orbital velocities in $\mathrm{n}^{\text {th }}$ and…

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
  1. $\mathrm{p}: \mathrm{n}$
  2. $\mathrm{n}: \mathrm{p}$
  3. $\mathrm{p}^2: \mathrm{n}^2$
  4. $\mathrm{n}^2: \mathrm{p}^2$

Solution

Velocity of electron in $n^{\text {th }}$ orbit of hydrogen atom, $\mathrm{V}_{\mathrm{n}}=\frac{\mathrm{e}^2}{2 \varepsilon_0 \mathrm{hn}}$ $\begin{array}{ll} \therefore & \mathrm{V}_{\mathrm{n}} \propto \frac{1}{\mathrm{n}} \\ \therefore & \frac{\mathrm{~V}_{\mathrm{p}}}{\mathrm{~V}_{\mathrm{n}}}=\frac{\mathrm{n}}{\mathrm{p}} \end{array}$

Asked in: MHT CET 2024 (09 May Shift 2)

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