JEE PYQ: Units And Dimensions Question 3
Question 3 - 2021 (25 Feb Shift 2)
If $e$ is the electronic charge, $c$ is the speed of light in free space and $h$ is Planck’s constant, the quantity $\frac{1}{4\pi\varepsilon_0} \frac{|e|^2}{hc}$ has dimensions of:
(1) $[LC^{-1}]$
(2) $[M^0 L^0 T^0]$
(3) $[M L T^0]$
(4) $[M L T^{-1}]$
Show Answer
Answer: (2)
Solution
The quantity $\frac{e^2}{4\pi\varepsilon_0 hc}$ is the fine structure constant, which is dimensionless $= [M^0 L^0 T^0]$.
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