- #1

jg370

jg said:The problem I am working on is as follows:

Consider an atom with a single electron in orbit of radius r about a nuclear charge +Ze.

As requested, I have dertermine that the electric potential energy of the nucleus at the electron position and the potential energy of the electron are respectively:

[tex]V(r) = \frac{1}{{4\pi\varepsilon_o}}\frac{Ze}{r}[/tex]

and

[tex]PE(elect) = \frac{Ze}{{4\pi\varepsilon_o r}}[/tex]

Next, I am asked to use the Coulomb law for interaction between the orbiting electron and the nucleus and write Newton's second law of motion for the orbiting electron.

For this part of the problem, I have come up with:

[tex]F(elect) = F(cent)[/tex], which implies,

[tex]-\frac{Ze}{{4\pi\varepsilon_o r}} = m\frac{v^2}{2}[/tex]

My difficulty arises as I am asked to show that:

[tex]KE = -\frac{1}{2}PE[/tex]

Could someone give me a hint how to proceed with this part of the problem?

Thank you kindly,

jg