Probing Nuclei with Electron Scattering

[TomCass]

Homework Statement

To study the structure of the lead nucleus, electrons are fired 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 R.

(Successfully completed) A. Find the acceleration of an electron at a distance of n R from the center of a lead nucleus.
Use ϵ_0 for the permittivity of free space, e for the magnitude of the charge on an electron, and m_e for the mass of an electron.

(Successfully completed) B. Find the acceleration of an electron at a distance of R from the center of a lead nucleus.

(Stumped, for some reason) C. Find the acceleration of an electron at a distance of R/ n from the center of a lead nucleus.

Homework Equations

F=qE

E=1/4pi(epsilon_naught)*q/r^2

a=F/m

The Attempt at a Solution

For example, this is what the solution to A is: [82(e)^2]/4(pi)(epsilon_naught)(m_e)(nR)^2

It seems to me that C should be the exact same process for A except with (R/n) instead of (nR). This is not correct. I was wondering if someone had a hint as to whether or not R now being divided would have an impact on an earlier calculation.

Any help is greatly appreciated! Thanks a bunch! And if I didn't clarify something enough in the explanation, feel free to ask!

 

[Curious3141]

Homework Statement

To study the structure of the lead nucleus, electrons are fired 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 R.

(Successfully completed) A. Find the acceleration of an electron at a distance of n R from the center of a lead nucleus.
Use ϵ_0 for the permittivity of free space, e for the magnitude of the charge on an electron, and m_e for the mass of an electron.

(Successfully completed) B. Find the acceleration of an electron at a distance of R from the center of a lead nucleus.

(Stumped, for some reason) C. Find the acceleration of an electron at a distance of R/ n from the center of a lead nucleus.

Homework Equations

F=qE

E=1/4pi(epsilon_naught)*q/r^2

a=F/m

The Attempt at a Solution

For example, this is what the solution to A is: [82(e)^2]/4(pi)(epsilon_naught)(m_e)(nR)^2

It seems to me that C should be the exact same process for A except with (R/n) instead of (nR). This is not correct. I was wondering if someone had a hint as to whether or not R now being divided would have an impact on an earlier calculation.

Any help is greatly appreciated! Thanks a bunch! And if I didn't clarify something enough in the explanation, feel free to ask!

It makes a huge difference within the boundary of the nucleus. What does Gauss' law say exactly?

Have you done problems dealing with the gravitational field strength *within* the earth? Same principle.