The ratio of the velocity of the electron in the first Bohr orbit to that in the second Bohr orbit of…
The ratio of the velocity of the electron in the first Bohr orbit to that in the second Bohr orbit of hydrogen atom is
- $8: 1$
- $2: 1$
- $4: 1$
- $1: 4$
Solution
Velocity of electron in the $\mathrm{n}^{\mathrm{th}}$ orbit $\mathrm{y}_{\mathrm{n}}=\frac{\mathrm{Ze}^2}{2 \varepsilon_0 \mathrm{nh}}$
$\begin{aligned}
& \Rightarrow \mathrm{v}_{\mathrm{n}} \propto \frac{1}{\mathrm{n}} \\
& \quad \text { given } \mathrm{n}_1=1 \text {, and } \mathrm{n}_2=2, \\
& \therefore \quad \frac{\mathrm{v}_1}{\mathrm{v}_2}=\frac{\mathrm{n}_2}{\mathrm{n}_1}=\frac{2}{1}
\end{aligned}$
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Asked in: MHT CET 2023 (10 May Shift 2)
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