# Question #def40

##### 1 Answer

#### Answer:

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,

while the kinetic energy is

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

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.