How far apart must two protons be if the electrical force of repulsion acting on either one is equal to its weight.

To determine how far apart two protons must be for the electrical force of repulsion to be equal to their weight, we need to use the equation for the electrical force between two charged particles. Let's break down the problem step by step:

1. Determine the electrical force of repulsion between two protons:
The electrical force between two point charges can be calculated using Coulomb's Law:
F = (k * q1 * q2) / r^2
where F is the electrical force, k is the electrostatic constant (8.99 x 10^9 N m^2/C^2), q1 and q2 are the charges of the two particles, and r is the distance between them.

In this case, both protons have the same charge, which is the elementary charge (e) of +1.6 x 10^-19 C. So, substituting the values, the electrical force between two protons is:
F = (k * e * e) / r^2

2. Determine the weight of a proton:
The weight of an object can be determined using the equation:
Weight = mass * acceleration due to gravity
The mass of a proton is approximately 1.67 x 10^-27 kg, and the acceleration due to gravity is approximately 9.8 m/s^2 on the surface of the Earth. Therefore, the weight of a proton is:
Weight = (1.67 x 10^-27 kg) * (9.8 m/s^2)

3. Set the electrical force equal to the weight and solve for the distance:
Setting the electrical force of repulsion equal to the weight and rearranging the equation, we have:
(k * e * e) / r^2 = (1.67 x 10^-27 kg) * (9.8 m/s^2)
Solving for r:
r = sqrt((k * e * e) / ((1.67 x 10^-27 kg) * (9.8 m/s^2)))

Now we can plug in the values and calculate the distance.

Note: When plugged into the formula, the numerical values can be quite large, so it may be more convenient to use scientific notation or a calculator.

Remember, it's important to ensure consistent units throughout the calculations for accurate results.