MHT CET · Physics · Atomic Physics
The ratio of speed of an electron in the ground state in the Bohr's first orbit of hydrogen atom to velocity of light (c) is (h \(=\) Planck's constant, \(\epsilon_{0}=\) permittivity of free space, \(\mathrm{e}=\) charge on electron \()\)
- A \(\frac{2 \mathrm{e}^{2} \in_{0}}{\mathbf{h} \mathbf{C}}\)
- B \(\frac{2 \in_{0} h c}{e^{2}}\)
- C \(\frac{e^{2}}{2 \in_{0} h c}\)
- D \(\frac{e^{3}}{2 E_{0} h c}\)
Answer & Solution
Correct Answer
(C) \(\frac{e^{2}}{2 \in_{0} h c}\)
Step-by-step Solution
Detailed explanation
The velocity of electron in Bohr's first orbit is
\(
\begin{aligned}
\mathrm{V} &=\frac{\mathrm{e}^{2}}{2 \varepsilon_{0} \mathrm{~h}} \\
\therefore \frac{\mathrm{V}}{\mathrm{c}} &=\frac{\mathrm{e}^{2}}{2 \varepsilon_{0} \mathrm{hc}}
\end{aligned}
\)
\(
\begin{aligned}
\mathrm{V} &=\frac{\mathrm{e}^{2}}{2 \varepsilon_{0} \mathrm{~h}} \\
\therefore \frac{\mathrm{V}}{\mathrm{c}} &=\frac{\mathrm{e}^{2}}{2 \varepsilon_{0} \mathrm{hc}}
\end{aligned}
\)
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