Question

The dimensions of $\frac{e^2}{4\pi {\omega }_{0}hc}$, where e, ${\omega }_0,h$ 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. $\left[M^1{L}^0{T}^0\right]$
• 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

$\left[M^0{L}^0{T}^0\right]$

$\left[e\right]=\left[AT\right],{\in }_0=\left[M^{-1}{L}^{-3}{T}^4{A}^2\right],\left[h\right]=\left[M{L}^2{T}^{-1}\right]$

and $\left[c\right]=\left[L{T}^{-1}\right]$

$\therefore \left[\frac{e^2}{4\pi {\in }_{0}hc}\right]=\left[\frac{A^2{T}^2}{M^{-1}{L}^{-3}{T}^4{A}^2\times M{L}^2{T}^{-1}\times L{T}^{-1}}\right]$

$=\left[M^0{L}^0{T}^0\right]$