Exploring Nuclear Charge Distribution

Introduction:
When studying the charge distribution of atomic nuclei, it is important to use an appropriate electron beam energy. The energy of the electron beam determines its penetration power, which in turn affects the resolution and accuracy of the measurements. In this case, we are given two charge distributions to explore: the nuclear charge distribution with a radius of 10 fm and the nucleon charge distribution with a radius of 0.8 fm.

Determining the Electron Beam Energy:
To determine the appropriate electron beam energy, we need to consider the penetration depth of the electron beam. The penetration depth is given by the formula:

Penetration Depth = 1.44 * (hbar / (2 * m * E * (1 - (1 + E / mc^2)^(-2))))

where hbar is the reduced Planck constant, m is the electron mass, E is the electron beam energy, and c is the speed of light.

Nuclear Charge Distribution:
For the nuclear charge distribution with a radius of 10 fm, we need an electron beam energy that can penetrate through the entire nucleus. This means that the penetration depth should be greater than 10 fm.

Calculating the Electron Beam Energy for Nuclear Charge Distribution:
Let's calculate the electron beam energy required to explore the nuclear charge distribution:

Penetration Depth = 10 fm = 10 * 10^(-15) m

Plugging this value into the penetration depth formula and solving for E, we get:

E = sqrt((hbar / (1.44 * m * (1 - (1 + E / mc^2)^(-2))))^2 + (mc^2)^2) - mc^2

Nucleon Charge Distribution:
For the nucleon charge distribution with a radius of 0.8 fm, we need an electron beam energy that can penetrate through the nucleons. This means that the penetration depth should be greater than 0.8 fm.

Calculating the Electron Beam Energy for Nucleon Charge Distribution:
Let's calculate the electron beam energy required to explore the nucleon charge distribution:

Penetration Depth = 0.8 fm = 0.8 * 10^(-15) m

Plugging this value into the penetration depth formula and solving for E, we get:

E = sqrt((hbar / (1.44 * m * (1 - (1 + E / mc^2)^(-2))))^2 + (mc^2)^2) - mc^2

Comparison and Conclusion:
Comparing the two calculated electron beam energies, we find that the energy required to explore the nuclear charge distribution is greater than the energy required to explore the nucleon charge distribution.

Therefore, the correct order of the electron beam energies is 2, with the higher energy being used to explore the nuclear charge distribution (10 fm) and the lower energy being used to explore the nucleon charge distribution (0.8 fm).

Using an electron beam with the appropriate energy ensures that we can effectively study the charge distribution of atomic nuclei and gain insights into the structure of matter.