Question

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

• A. $\left[ M ^{0} L ^{0} T ^{0}\right]$
• B. $\left[ ML ^{0} T ^{0}\right]$
• C. $\left[ M ^{0} LT ^{0}\right]$
• D. $\left[ M ^{0} L ^{0} T\right]$

Answer 1

Answer: (A)

$[e]=A T, \varepsilon_{0}=\left[ M ^{-1} L ^{-3} T ^{4} A ^{2}\right]$
$[h]=\left[ ML ^{2} T ^{-1}\right]$ and $[c]=\left[ LT ^{-1}\right]$
$\therefore \left[\frac{e^{2}}{4 \pi \varepsilon_{0} h c}\right]$
$=\left[\frac{A^{2} T^{2}}{M^{-1} L^{-3} T^{4} A^{2} \times M L^{2} T^{-1} \times L T^{-1}}\right]$
$=\left[M^{0} L^{0} T^{0}\right]$