Question

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

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

Answer 1

Correct Answer - B
If `a= 0`, the total charge on the nucleous is given by
` Q = int rho _r 2 pi r^2 dr`
Now `d/R = (rho_r)/(R-r)`
or `rho_r = d/R (R-r)`
`:. Q= int _0^R d/R (R -r) 4 pi r^2 dr = (pi dR^3)/3`
Since `Q= Ze rArr (pi dR^3)/3 = Ze 3, d = (3 Ze)/(pi R^3)`.