The size of Rutherford's atom is about 0.1 nm.

(a) Calculate the attractive electrostatic force between an electron and a proton at that distance.

(b) Calculate the electrostatic potential energy of that atom. Express the result in unit eV.

(c) The size of Rutherford's atomic nucleus is about 1 fm. Calculate the repulsive electrostatic force between two protons at that distance.

(d) Calculate the electrostatic potential energy of a pair of protons in such a nucleus. Express the result in unit MeV.

a) & c) F = kq^2/r^2

b) & d) PE = kq^2/r

To calculate the attractive electrostatic force between an electron and a proton, we can use Coulomb's Law. Coulomb's Law states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

(a) To calculate the attractive electrostatic force between an electron and a proton at a distance of 0.1 nm:

1. Determine the charges involved:
The charge of an electron is approximately -1.6 x 10^-19 coulombs.
The charge of a proton is approximately +1.6 x 10^-19 coulombs.

2. Calculate the force:
The formula for Coulomb's Law is F = (k * q1 * q2) / r^2, where F is the force, k is the electrostatic constant (approximately 9 x 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between them.

Plugging in the values:
F = (9 x 10^9 Nm^2/C^2) * ((-1.6 x 10^-19 C) * (1.6 x 10^-19 C)) / (0.1 x 10^-9 m)^2

Calculating this expression will give you the value of the attractive electrostatic force between the electron and proton.

(b) To calculate the electrostatic potential energy of that atom:

1. Use the formula for electrostatic potential energy:
The formula for electrostatic potential energy is U = (k * q1 * q2) / r, where U is the potential energy, k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between them.

2. Calculate the potential energy:
U = (9 x 10^9 Nm^2/C^2) * ((-1.6 x 10^-19 C) * (1.6 x 10^-19 C)) / (0.1 x 10^-9 m)

Remember to consider the signs and units to obtain the correct result for the electrostatic potential energy. Convert the units, if necessary.

(c) To calculate the repulsive electrostatic force between two protons at a distance of 1 fm:

1. Determine the charges involved:
The charge of a proton is approximately +1.6 x 10^-19 coulombs.

2. Calculate the force:
Using Coulomb's Law, F = (k * q1 * q2) / r^2, where F is the force, k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between them.

Plugging in the values:
F = (9 x 10^9 Nm^2/C^2) * ((1.6 x 10^-19 C) * (1.6 x 10^-19 C)) / (1 x 10^-15 m)^2

Calculating this expression will give you the value of the repulsive electrostatic force between the two protons.

(d) To calculate the electrostatic potential energy of a pair of protons in such a nucleus:

1. Use the formula for electrostatic potential energy:
U = (k * q1 * q2) / r, where U is the potential energy, k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between them.

2. Calculate the potential energy:
U = (9 x 10^9 Nm^2/C^2) * ((1.6 x 10^-19 C) * (1.6 x 10^-19 C)) / (1 x 10^-15 m)

Remember to consider the signs and units to obtain the correct result for the electrostatic potential energy. Convert the units, if necessary, to express the result in MeV (mega-electron volts), where 1 MeV = 1.6 x 10^-13 J.