Question

The dimension of $\frac{ e ^{2}}{4 \pi \varepsilon_{0} hc },$ where $e , \varepsilon_{0}, h$ and $c$ are electric 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)

We know that, $[ e ]=[ AT ]$,
$\left[\varepsilon_{0}\right]=\left[ M ^{-1} L ^{-3} T ^{4} A ^{2}\right]$,
$ \therefore \left[\frac{ e ^{2}}{4 \pi \varepsilon_{0} hc }\right] $
$=\left[\frac{ A ^{2} T ^{2}}{ M ^{-1} L ^{-3} T ^{4} A ^{2} \times ML ^{2} T ^{-1} \times LT ^{-1}}\right]$
$=\left[ M ^{0} L ^{0} T ^{0}\right] $