# Question #def40

Jan 9, 2017

If I am interpreting the question correctly, the answer is that the kinetic energy is +3.6 eV.

#### Explanation:

Here's the reason:

It can be shown (although the proof is lengthy, and I'm not certain you are asking to see it!), that for an electron in a bound state with a Coulomb potential acting, the potential energy is negative and has twice the absolute value of the kinetic energy.

Specifically, $V = - \left(\frac{1}{4 \pi {\epsilon}_{o}}\right) \frac{1}{r}$

while the kinetic energy is

$K = \left(\frac{1}{4 \pi {\epsilon}_{o}}\right) \frac{1}{2 r}$

When you add these two quantities together, you get the total energy, which is

$E = - \left(\frac{1}{4 \pi {\epsilon}_{o}}\right) \frac{1}{2 r}$

Note that the only difference in these last two expressions in the sign; the kinetic energy is necessarily positive, while the total energy is negative, indicating a bound state of electron within the atom.

So, the kinetic energy and the total energy have the same absolute value, but the total energy is -3.6 eV while the kinetic energy is +3.6 eV.