Determine the effective nuclear charge

[patm95]

1. Homework Statement

The 3s state of Na has an energy of -5.14 eV. Determine the effective nuclear charge.

2. Homework Equations

Zeffective = Z - S (not listed in textbook, found this online when trying to figure out the problem)

3. The Attempt at a Solution

Nothing in the textbook in this section talk about determining nuclear charge. I know that Na is in the 2s^2 2p^6 group

 

[nickjer]

What is the binding energy for an electron in a hydrogen atom? Then you can ask what is the binding energy for a single electron with a nuclear charge of +Z.

Now you can pretend that you have something similar here, where the core electrons are shielding some of the nuclear charge of Na. You have know idea how much effective nuclear charge the single electron feels outside, so knowing the binding energy you can work backwards to get this effective nuclear charge.