Physics And Measurement Question 204
Question: The dimension of $ e^{2}/4\pi {\varepsilon _{2}}hc, $ where $ e,{\varepsilon _{0}},h $ and c are electronic charge, electric permittivity, Planck’s constant and velocity of light in vacuum, respectively, is
Options:
A) $ [M^{0}L^{0}T^{0}] $
B) $ [M^{1}L^{0}T^{0}] $
C) $ [M^{0}L^{1}T^{0}] $
D) $ [M^{0}L^{0}T^{1}] $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ [e]=[AT],L _{0}=[{{M}^{-1}}{{L}^{-3}}T^{4}A^{2}] $ = $ [ML^{2}{{T}^{-1}}] $
and $ [c]=[L{{T}^{-1}}] $
$ [ \frac{e^{2}}{4\pi {\in _{0}}hc} ]=[ \frac{A^{2}T^{2}}{{{M}^{-1}}{{L}^{-3}}T^{4}A^{2}\times ML^{2}{{T}^{-1}}\times L{{T}^{-1}}} ] $
$ =[M^{0}L^{0}T^{0}] $
