# Given the ionization energy, find the number of protons

1. Sep 10, 2011

### Quantum Mind

1. The problem statement, all variables and given/known data

A hydrogen like system has ionization energy of 11808 kJ/mol. Find the number of protons in the nucleus.

2. Relevant equations

Not sure.

Should I use the formula En = E1/n2?

3. The attempt at a solution

The ionization energy of H is 1312 kJ/mol. The ionization energy of the system is 11808 kJ/mol. Since this is hydrogen like system, it has only one electron in its outer shell and so the effects of electron repulsion can be ruled out. If I try to use the above formula, I am not getting the answer. Or should I use the complicated formula for total energy of the system and then try to find z from it?

2. Sep 10, 2011

### kuruman

Not quite. Try En=-Z2E1/n2.

3. Sep 10, 2011

### Spinnor

4. Sep 10, 2011

### Quantum Mind

Thanks, but how do I find Z ?

En = 11808
E1 = 1312
Z = ?
n = ? (Is it the number of electrons in the outer shell? In that case it would be 1)

What to do with the negative sign ?

5. Sep 10, 2011

### Quantum Mind

@ Spinnor: Thanks for the link. I posted before viewing your post.

Guess n = 1 and then it works out (at least I think so)

En = E1 * Z2/n2

11808/1312 = Z2

Z = 3, which incidentally is the right answer.

Is my working correct?

6. Sep 10, 2011

### kuruman

Z is the number of protons in the nucleus of this atom and n is the lowest energy level from which you remove an electron when you ionize it. In this case n = 1. Do nothing with the negative sign. It just means that you need to add energy to the atom in order to ionize it, i.e. end up with a nucleus and an electron separate from one another.

7. Sep 10, 2011

### kuruman

That is correct.

8. Sep 10, 2011

### Quantum Mind

Thank You, kuruman.