The radius of a gold nucleus (Z = 79) is about 7.0 × 10–15 m. Assume that the positive charge is distributed uniformly throughout the nuclear volume. Find the strength of the electric field at

(a) the surface of the nucleus and


(b) at the middle point of a radius.


Remembering that gold is a conductor, is it justified to assume that the positive charge is uniformly distributed over the entire volume of the nucleus and does not come to the outer surface?



Given:


Radius of gold nucleus=7.0× 10-15m=r


Charge on the nucleus=79× 1.6× 10-19C=q


(a)


Consider a gaussian spherical surface of radius of the nucleus=r


By symmetry all points on this surface are equivalent and electric field at all points have same magnitude and is in radial direction


Therefore flux passing through this surface is given by


…(i)


We know that,


By Gauss’s law, flux of net electric field (E⃗ ) through a closed surface S equals the net charge enclosed (qin) by the surface divided by ϵ0



Charge enclosed by this sphere =total charge on the nucleus=q


Using gauss’s law and eqn.(i)




Putting the values of r,q and ϵ0



N/C


Therefore the strength of electric field at the surface of nucleus is 2.31× 1021N/C


(b)for calculating electric field at middle point of radius consider similar gaussian surface with radius half of that of nucleus=r/2


Charge enclosed by volume =Q


Charge enclosed by volume Q’


We get



Using gauss law and eqn.(i)




N/C


N/C


Therefore electric field at middle point of radius of nucleus is given by 1.16× 1021N/C


We know that when electric charge is given to a conductor it comes on its surface


But nucleons are bound by strong nuclear force inside nucleus which holds them and prevents them from coming out of conductor.


Therefore it is justified to assume that electric charge is uniformly distributed in its entire volume.


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