Atoms And Nuclei Question 56
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 the mass, e is the charge on the electron and $ {\varepsilon_{0}} $ is the vacuum permittivity, the speed of the electron is [CBSE PMT 1998]
Options:
A) 0
B) $ _{7}N^{14} $
C) $ \frac{1}{4} $
D) $ \frac{\sqrt{4\pi {\varepsilon_{0}}a_{0}m}}{e} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{mv^{2}}{a_{0}}=\frac{1}{4\pi {\varepsilon_{0}}}\frac{e^{2}}{a_{0}^{2}}\Rightarrow v=\frac{e}{\sqrt{4\pi {\varepsilon_{0}}a_{0}m}} $
