Atoms And Nuclei Question 118
Question: The ratio of speed of an electron in ground state in Bohrs first orbit of hydrogen atom to velocity of light in air is [MH CET 2002]
Options:
A) $ \frac{e^{2}}{2{\varepsilon_{0}}hc} $
B) $ \frac{2e^{2}{\varepsilon_{0}}}{hc} $
C) $ \frac{e^{3}}{2{\varepsilon_{0}}hc} $
D) $ \frac{2{\varepsilon_{0}}hc}{e^{2}} $
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Answer:
Correct Answer: A
Solution:
Speed of electron in nth orbit (in CGS) $ v_{n}=\frac{2\pi Ze^{2}}{nh} $ (k = 1) For first orbit $ H_{2} $ ; n = 1 and Z = 1 So $ v=\frac{2\pi e^{2}}{h} $
Þ $ \frac{v}{c}=\frac{2\pi e^{2}}{hc} $
