Question

If $e,{ϵ}_0,h$ and $c$ respectively represents electric charge, permittivity of free space, Planck's constant and speed of light. The dimension of $\frac{e^2}{4\pi {ϵ}_{0}hc}$ is :

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

Answer 1

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

Planck's constant (h) has joule-seconds unit, dimensions are $=\left[M{L}^2{T}^{-1}\right]$

Electron charge (e) will have $\left[TI\right]$

Dimension for ${\epsilon }_0$ is $\left[M^{-1}{L}^{-3}{T}^4{I}^2\right]$

Dimensions for $\frac{e^2}{4\pi {\epsilon }_{0}hc}$ will be$\left[M^0{L}^0{T}^0\right]$.