The dimensions of the quantity namely `(mu_(0)ce^(2))/(2h)` where `mu_(0)` permeability of free space, c - velocity of light, e - electronic charge and `h = (h)/(2pi)` being Planck's constant

Options

A. `[M^(0)LT]`
B. `[M^(0)L^(0)T]`
C. `[M^(0)L^(0)T^(0)]`
D. `[M^(-2)L^(-1)T^(-3)]`

Answer

C

Explanation

The quantity is `(mu_(0)ce^(2))/(2h)= (pimu_(0)ce^(2))/(h)`
`:. c= (1)/(sqrt(mu_(0)epsilon_(0))` or `c^(2)= (1)/(mu_(0)epsilon_(0))`
`:. cmu= (1)/(cepsilon_(0)) :. (pimu_(0)ce^(2))/(h)= (pie^(2))/(cepsilon_(0)h)`
`:. F= (1)/(4piepsilon_(0))(e^(2))/(r^(2))` or `(e^(2))/(r^(2))= Fe^(2)4pi :. (pie^(2))/(cepsilon_(0)h)= (Fr^(2))/(ch) xx 4pi^(2)`
The dimensions of
`(Fr^(2))/(ch)= ([MLT^(-2)][L^(2)])/([LT^(-1)][ML^(2)T^(-1)])= ([ML^(3)T^(-2)])/([ML^(3)T^(-2)])= [M^(0)L^(0)T^(0)]`