# Probing Nuclei with Electron Scattering

• TomCass
In summary, the lead nucleus structure is studied by firing electrons at a lead target and measuring the deflection caused by the nucleus's charge. The acceleration of an electron at different distances from the center of the lead nucleus is calculated using the equations F=qE, E=1/4pi(epsilon_naught)*q/r^2, and a=F/m. While the calculation for A (at a distance of nR) is correct, the calculation for C (at a distance of R/n) is not the same and Gauss' law must be considered. This is similar to calculating the gravitational field strength within the Earth.
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!

Last edited:
TomCass said:

## 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.

## 1. What is electron scattering?

Electron scattering is a technique used in nuclear physics to probe the internal structure of atomic nuclei. It involves firing high-energy electrons at a target nucleus and measuring the scattered electrons to gather information about the structure and properties of the nucleus.

## 2. How does electron scattering work?

Electron scattering works by accelerating electrons to high energies using a particle accelerator. These electrons are then directed towards a target nucleus, where they interact with the protons and neutrons in the nucleus. The scattered electrons are then measured and analyzed to determine the characteristics of the nucleus.

## 3. What can we learn from probing nuclei with electron scattering?

We can learn a variety of information about the structure and properties of atomic nuclei through electron scattering. This includes the size, shape, and distribution of protons and neutrons within the nucleus, as well as the nuclear forces that hold the nucleus together.

## 4. How is electron scattering different from other nuclear probes?

Electron scattering is different from other nuclear probes, such as alpha or beta decay, because it is a non-destructive method. This means that the target nucleus remains intact after the scattering process, allowing for multiple measurements to be taken. Additionally, electron scattering can provide more detailed information about the internal structure of the nucleus compared to other probes.

## 5. What are the practical applications of probing nuclei with electron scattering?

Probing nuclei with electron scattering has many practical applications in various fields, including nuclear energy, medical imaging, and materials science. By understanding the structure and properties of atomic nuclei, we can develop more efficient and safe nuclear reactors, improve diagnostic techniques for medical imaging, and create new materials for various purposes.

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