Question

If $e$ is the electric charge of an electron, $c$ is the speed of light in free space, and $h$ is planck's constant, ${ϵ}_0$ is permittivity of free space. The dimension of $\frac{e^2}{4\pi {ϵ}_{0}hc}$ is

• A. $\left[L{C}^{-1}\right]$
• B. $\left[M^0{L}^0{T}^0\right]$
• C. $\left[ML{T}^0\right]$
• D. $\left[ML{T}^{-1}\right]$

Answer 1

The correct option is B $\left[M^0{L}^0{T}^0\right]$

Given,
$e=$ Electric charge of an electron $=\left[TI\right]$
$c=$ Speed of Light $=\left[M^0{L}^1{T}^{-1}\right]$
$h=$ Planck's constant $=\left[M{L}^2{T}^{-1}\right]$
${ϵ}_0=\left[M^{-1}{L}^{-3}{T}^4{I}^2\right]$
Therefore dimension of $\frac{e^2}{4\pi ϵhc}$ is $\left[M^0{L}^0{T}^0\right]$