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The nuclear charge (Ze) is non uniformll...

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

(a) `(3Ze)/(4piR^3)`

B

(b) `(3Ze)/(piR^3)`

C

(c) `(4Ze)/(3piR^3)`

D

(d) `(Ze)/(3piR^3)`

Text Solution

Verified by Experts

The correct Answer is:
B
For `a=0`, the graph is as shown. The equation for the graph line is
`rho=d-r/Rdr`


The charge in the dotted element shown in fig is `dq=rhoxx4pir^2dr`
`:.` `dq=(d-d/Rr)4pir^2drimpliesZe=int_0^R4pidr^2-int_0^R(4pid)/(R)r^3dr`
`Ze=4pid(R^3)/(3)-(4pid)/(R)(R^4)/(4)`
`:.` `(Ze)/(4pidR^3)=1/3-1/4=1/12` `:.` `d=(3Ze)/(piR^3)`
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