Atoms And Nuclei Question 101
Question: The ratio of the speed of the electron in the first Bohr orbit of hydrogen and the speed of light is equal to (where e, h and c have their usual meanings) [MP PMT 2000]
Options:
A) $ 2\pi hc/e^{2} $
B) $ e^{2}h/2\pi c $
C) $ e^{2}c/2\pi h $
D) $ 2\pi e^{2}/hc $
Show Answer
Answer:
Correct Answer: D
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} $
