The ratio of speed of an electron in the ground state in the Bohr's first orbit of hydrogen atom to velocity…

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 $)$
  1. $\frac{2 \mathrm{e}^{2} \in_{0}}{\mathbf{h} \mathbf{C}}$
  2. $\frac{2 \in_{0} h c}{e^{2}}$
  3. $\frac{e^{2}}{2 \in_{0} h c}$
  4. $\frac{e^{3}}{2 E_{0} h c}$

Solution

The velocity of electron in Bohr's first orbit is $\begin{aligned} \mathrm{V} &=\frac{\mathrm{e}^{2}}{2 \varepsilon_{0} \mathrm{~h}} \\ \therefore \quad \frac{\mathrm{V}}{\mathrm{c}} &=\frac{\mathrm{e}^{2}}{2 \varepsilon_{0} \mathrm{hc}} \end{aligned}$

Asked in: MHT CET 2020 (16 Oct Shift 1)

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