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

The dimensions of the quantity namely (mu_(0)ce^(2))/(2h)where mu_(0)

1.	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
Answer» `[M^(0)LT]` `[M^(0)L^(0)T]` `[M^(0)L^(0)T^(0)]` `[M^(-2)L^(-1)T^(-3)]` Solution :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)]`