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