The dimensional formula of a physical quantity represented by e ^2 4 ₀ ~h is [e is the charge of electron, ₀ is the permittivity of free space, and h is the Planck's constant]

Step-by-step solution

e ^2=[ q ]^2=[ AT ]^2= [ A ^2 ~T ^2 ] aligned & h = E v = [ ML ^2 ~T ⁻² ] [ T ⁻¹ ] = [ ML ^2 ~T ⁻¹ ] & ₀= 1 4 F q ^2 r ^2 = [ A ^2 ~T ^2 ] [ MLT ⁻² ] [ L ^2 ] = [ M ⁻¹ ~L ⁻³ ~T ^4 ~A ^2 ] & e ^2 4 ₀ ~h = [ A ^2 ~T ^2 ] [ M ⁻¹ ~L ⁻³ ~T ^4 ~A ^2 ] [ ML ^2 ~T ⁻¹ ] = [ L T ⁻¹ ] aligned