In the Bohr model of hydrogen atom, the centripetal force is furnished by the coulomb attraction between the…

In the Bohr model of hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and the electron. If ' $r_0$ ' is the radius of the ground state orbit, ' m ' is the mass, 'e' is the charge on the electron and ' $\varepsilon_0$ ' is the permittivity of vacuum, the speed of the electron is
  1. zero
  2. $\frac{\mathrm{e}}{\sqrt{\varepsilon_0 \mathrm{r}_0 \mathrm{~m}}}$
  3. $\frac{\mathrm{e}}{\sqrt{4 \pi \varepsilon_0 \mathrm{r}_0 \mathrm{~m}}}$
  4. $\frac{\sqrt{4 \pi \varepsilon_0 \mathrm{r}_0 \mathrm{~m}}}{\mathrm{e}}$

Solution

Given, Centripetal Force $=$ Coulomb attraction $\begin{aligned} & \frac{\mathrm{mv}^2}{\mathrm{r}_0}=\frac{\mathrm{l}}{4 \pi \varepsilon_0} \frac{\mathrm{e}^2}{\mathrm{r}_0^2} \\ \therefore \quad & \mathrm{v}=\frac{\mathrm{e}}{\sqrt{4 \pi \varepsilon_0 \mathrm{r}_0 \mathrm{~m}}} \end{aligned}$

Asked in: MHT CET 2024 (10 May Shift 2)

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