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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

`( 3 Ze)/(4 pi R^(3))`

B

`(3Ze)/(pi R^(3))`

C

`( 4Z e)/( 3pi R^(3))`

D

`(Ze)/(3pi R^(3))`

Text Solution

Verified by Experts

The correct Answer is:
B
For `a=0rArrp(r)=(-d/r.r+d)`
Now, `int_(0)^(r)(4pir^(2))(d-d/Rr)dr=`net charge =ze
Solving this equation, we get `d=(3ze)/(piR^(3))`
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