Question

The hydrogen atom contains a proton, mass 1.67 10-27 kg, and an electron, mass 9.11 10-31 kg. The average distance between them is 5.3 10-11 m. The charge of the proton is the same size, opposite sign of the electron.

a)What is the magnitude of the average electrostatic attraction between them?

F=kqq/d^2

You would have to convert from kg to C, correct? Then, plug everything into the formula.

b)What is the magnitude of the average gravitational attraction between them?

I am drawing a complete blank on the formula for this one and I cannot find it in my notes.

Answer 1

There are some mistakes in the problem. The average distance between the electron and the proton is not equal to 5.3 10^(-11) m. The distance
a = 5.3 10^(-11) m is the Bohr radius which and at this distance is the most likely distance for the electron to be.

The average distance is 3/2 a. In this problem you need to know the average of 1/d^2, which is given by 2/a^2. So, you need to find the charge of the electron, e, anbd evaluate:

2 k e^2/a^2

The average gravitational attraction is given by:

2 G m^2/a^2

Of course, the other mistake in this problem is that it is suggested that the average attractive force would be given by k e^2/a^2 :)