Atoms - Result Question 36

38. In the Bohr model of a hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and the electron. If $a_0$ is the radius of the ground state orbit, $m$ is the mass, $e$ is the charge on the electron and $\varepsilon_0$ is the vacuum permittivity, the speed of the electron is

[1998]

(a) 0

(b) $\frac{e}{\sqrt{\varepsilon_0 a_0 m}}$

(c) $\frac{e}{\sqrt{4 \pi \varepsilon_0 a_0 m}}$

(d) $\frac{\sqrt{4 \pi \varepsilon_0 a_0 m}}{e}$

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Answer:

Correct Answer: 38. (c)

Solution:

(c) Centripetal force $=$ Coulombian force

$\frac{m v^{2}}{a_0}=\frac{1}{4 \pi \varepsilon_0} \cdot \frac{e \times e}{a_0^{2}}$

$\Rightarrow v^{2}=\frac{e^{2}}{4 \pi \varepsilon_0 \cdot a_0 \cdot m} \Rightarrow v=\frac{e}{\sqrt{4 \pi \varepsilon_0 \cdot a_0 \cdot m}}$



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