Nuclear Physics And Radioactivity Question 25
Question: The ratio of the speed of the electrons in the ground state of hydrogen to the speed of light in vacuum is [MNR 1994; MP PMT 1994]
Options:
A) 1/2
B) 2/137
C) 1/137
D) 1/237
Show Answer
Answer:
Correct Answer: C
Solution:
Speed of electron in nth orbit of hydrogen atom $ v=\frac{e^{2}}{2{\varepsilon_{0}}n,h} $ In ground state n = 1
Þ $ v=\frac{e^{2}}{2{\varepsilon_{0}}h} $
Þ $ \frac{v}{c}=\frac{e^{2}}{2{\varepsilon_{0}}ch}=\frac{{{(1.6\times {{10}^{-19}})}^{2}}}{2\times 8.85\times {{10}^{-12}}\times 3\times 10^{8}\times 6.6\times {{10}^{-34}}} $ $ =\frac{1}{137} $ .
BETA
