The nuclear charge (`Ze`) is non uniformlly distribute with in a nucleus of radius `r`. The charge density `rho(r)` (charge per unit volume) is dependent only on the radial distance r form the centre of the nucleus s shown in figure. The electric field is only along the radial direction.

For a=0 the value of d (maximum value of `rho` as shown in the figure) is

Options

A. `(3Ze)/(4 piR^(3))`
B. `(3Ze)/(piR^(3))`
C. `(4Ze)/(3 pi R^(3))`
D. `(Ze)/(3 pi R^(3))`

Answer

B

Explanation

`rho` versus r graph for a`=0` will be as shown

`(d)/(R )=(rho)/(R-r)rArr rho=(d(R-r))/(R)` for `r leR`
`Q=Ze=underset(0)overset(R)int rho(4 pi x^(2))dx=(pi dR^(3))/(3)` or `d=(3Ze)/(piR^(3))`