The dimensions of (e2/4 π ε0 h c'), where e, ε0, h and c and c are electronic charge, electric permittivity Planck's constant and velocity of light in vacuum respectively

Question

The dimensions of (e2/4 π ε0 h c'), where e, ε0, h and c and c are electronic charge, electric permittivity Planck's constant and velocity of light in vacuum respectively (A) [ M 0 L 0 T 0] (B) [ ML 0 T 0] (C) [ M 0 LT 0] (D) [ M 0 L 0 T]

Tardigrade Admin · Accepted Answer

[e]=A T, ε0=[ M -1 L -3 T 4 A 2] [h]=[ ML 2 T -1] and [c]=[ LT -1] ∴ [(e2/4 π ε0 h c)] =[(A2 T2/M-1 L-3 T4 A2 × M L2 T-1 × L T-1)] =[M0 L0 T0]

Q. The dimensions of $\frac{e ^{2}}{4 π ε _{0} h c ^{'}}$ , where $e, ε_{0}, h$ and $c$ and $c$ are electronic charge, electric permittivity Planck's constant and velocity of light in vacuum respectively

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

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

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

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

$[e] = A T, ε_{0} = [M^{- 1} L^{- 3} T^{4} A^{2}]$
$[h] = [M L^{2} T^{- 1}]$ and $[c] = [L T^{- 1}]$
$∴ [\frac{e ^{2}}{4 π ε _{0} h c}]$
$= [\frac{A ^{2} T ^{2}}{M ^{- 1} L ^{- 3} T ^{4} A ^{2} \times M L ^{2} T ^{- 1} \times L T ^{- 1}}]$
$= [M^{0} L^{0} T^{0}]$

Q. The dimensions of 4πε0​hc′e2​, where e,ε0​,h and c and c are electronic charge, electric permittivity Planck's constant and velocity of light in vacuum respectively

[M0L0T0]

[ML0T0]

[M0LT0]

[M0L0T]