Atoms And Nuclei Question 273
Question: 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 he mass, e is the charge on the electron and $ {\varepsilon_{0}} $ is the vacuum permittivity, the speed of the electron is
Options:
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: C
Solution:
- Centripetal force = Colombian force $ \frac{mv^{2}}{a_{0}}=\frac{1}{4\pi {\varepsilon_{0}}}.\frac{e\times e}{a_{0}^{2}} $
$ \Rightarrow v^{2}=\frac{e^{2}}{4\pi {\varepsilon_{0}}.a_{0}.m}\Rightarrow v=\frac{e}{\sqrt{4\pi {\varepsilon_{0}}.a_{0}.m}} $
