The nucleus of a copper atom contains 29 protons and has a radius of 4.8*10^-15m. How much work (in electron volts) is done by the electric force as a proton is brought from infinity, where it is at rest, to the "surface" of a copper nucleus?
I really got no clue to do it. Can anyone please explain and help????THANKS A LOT!!!!
I would assume the protons are equally distributed in the nucleus. From that, you can get E at the surface,and E(r) outside the nucleus
Work= INT Eqdr Where E is a function of r.
i still don't really get it...Can you tell me more about it?
To calculate the work done by the electric force as a proton is brought to the surface of a copper nucleus, we can use the formula:
Work = Change in Potential Energy
1. First, let's calculate the change in potential energy. The potential energy of a charged particle in an electric field is given by:
Electric Potential Energy = (Charge of the particle) * (Electric Potential)
In this case, the charge of a proton is +1.6 x 10^-19 Coulombs. The electric potential is given by:
Electric Potential = (Electric Force) / (Charge of the proton)
2. Now, let's calculate the electric force. The electric force between two charged particles is given by:
Electric Force = (Coulomb constant) * [(Charge 1) * (Charge 2)] / [(Radius)^2]
In this case, the Coulomb constant is approximately equal to 9 x 10^9 N m^2 / C^2. We know the charge of the proton (+1.6 x 10^-19 C) and the radius of the copper nucleus (4.8 x 10^-15 m).
3. Substitute the values into the formulas and calculate the electric force.
4. Once you have the electric force, substitute it into the electric potential formula and calculate the electric potential.
5. Finally, substitute the charge of the proton and the electric potential into the formula for potential energy and calculate the change in potential energy.
6. Since the problem asks for the work done in electron volts, we need to convert the change in potential energy from joules to electron volts. The conversion is: 1 eV = 1.6 x 10^-19 J.
By following these steps, you can calculate the work done by the electric force as a proton is brought to the surface of a copper nucleus.