The dimensions of e^2 /4 _0hc, where e, , _0 , ,h and c are elect… - Vidyadip

MCQ

The dimensions of ${e^2}/4\pi {\varepsilon _0}hc$, where $e,\,{\varepsilon _0},\,h$ and $c$ are electronic charge, electric permittivity, Planck’s constant and velocity of light in vacuum respectively

✓
$[{M^0}{L^0}{T^0}]$
B
$[{M^1}{L^0}{T^0}]$
C
$[{M^0}{L^1}{T^0}]$
D
$[{M^0}{L^0}{T^1}]$

✓

Answer

Correct option: A.

$[{M^0}{L^0}{T^0}]$

a
(a) $[e] = [AT],$${ \in _0} = [{M^{ - 1}}{L^{ - 3}}{T^4}{A^2}],$ $[h] = [M{L^2}{T^{ - 1}}]$
and $[c] = [L{T^{ - 1}}]$

$\therefore $$\left[ {\frac{{{e^2}}}{{4\pi { \in _0}hc}}} \right] = \left[ {\frac{{{A^2}{T^2}}}{{{M^{ - 1}}{L^{ - 3}}{T^4}{A^2} \times M{L^2}{T^{ - 1}} \times L{T^{ - 1}}}}} \right]$

$ = [{M^0}{L^0}{T^0}]$

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