The dimensions of {e^2}/4pi {varepsilon _0}hc | vedclass

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Question

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

Vedclass · Accepted Answer

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

Vedclass · Answer

(a) $[e] = [AT],$${ \in _0} = [{M^{ - 1}}{L^{ - 3}}{T^4}{A^2}],$ $[h] = [M{L^2}{T^{ - 1}}]$
and $[c] = [L{T^{ - 1}}]$
$	herefore $$\left[ {\frac{{{e^2}}}{{4\pi { \in _0}hc}}} ight] = \left[ {\frac{{{A^2}{T^2}}}{{{M^{ - 1}}{L^{ - 3}}{T^4}{A^2} 	imes M{L^2}{T^{ - 1}} 	imes L{T^{ - 1}}}}} ight]$
$ = [{M^0}{L^0}{T^0}]$

	List $-I$		List $-II$
$A$.	Coefficient of Viscosity	$I$.	$[M L^2T^{–2}]$
$B$.	Surface Tension	$II$.	$[M L^2T^{–1}]$
$C$.	Angular momentum	$III$.	$[M L^{-1}T^{–1}]$
$D$.	Rotational Kinetic energy	$IV$.	$[M L^0T^{–2}]$

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

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$C$. Angular momentum $III$. $[M L^{-1}T^{–1}]$

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