A student determins a dimensionless quantities `B = (E^(n))/(2 epsilon_(0) hc)` Find the value of `n` (here, `e =` electric charge `epsilon_(0)` electric permittivety of vacume, `b =` Plank's constant and `c =` speed of light)`

Options

A. `3`
B. `4`
C. `2`
D. `1`

Answer

c

Explanation

Dimension of `B = [M^(0)L^(0)T^(0)]`
Dimension `e= [AT]`
Dimension `epsilon_(0)= [A^(2)M^(-1)L^(-3)T^(4)]`
Dimension `h = [ML^(2)T^(-1)]`
Dimension `c = [LT^(-1)]`
`:. [M^(0)L^(0)T^(0)]= ([AT]^(n))/([A^(2)M^(-1)L^(-3)T^(4)][ML^(2)T^(-1)] [LT^(-1)])`
`or [M^(0)L^(0)T^(0)] = [A^(n-2)L^(0)T^(n-2)]`
`:. n - 2= 0`
`rArr n = 2`