Problem 18.

To study the structure of the lead nucleus, electrons are fixed at a lead target. Some of the electrons actually enter the nuclei of the target, and the deflection of these electrons is measured. The deflection is caused by the charge of the nucleus, which is distributed approximately uniformly over the spherical volume of the nucleus. A lead nucleus has a charge of +82e ( ) and a radius of . Find the acceleration of an electron at the following distances from the center of a nucleus.

(a) R

(b) 2R

(c) R/2

(d) 0 (at the center)

Solution

In the present problem we have a uniformly charged sphere. The electric field of such sphere has the following expression (Q is the charge of the sphere):

Then the electric force on an electron is

The acceleration is the ratio of the force and the mass of the electron:

where .

Then

(a) at r=R:

(a) at r=2R:

(a) at r=R/2:

(a) at r=0: