# Homework Help: Why electron affinity of noble gas is endothermic?

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1. Oct 12, 2016

### NuclearBoofluff

The problem statement, all variables and given/known data
Why is the EA of Neon endothermic even though it has a high Z eff?
Basically, what makes a full valence shell so stable?

The attempt at a solution

I know it has to do with shielding, core e-, and valence e-. But I don't know how to word it.

2. Oct 13, 2016

### DrDu

A full valence shell is stable because it is full :-) Namely an additional electron can't be added to the valence shell but has to occupy an orbital of the next shell, which are energetically much higher because they have an additional radial node and therefore a higher kinetic energy.

3. Oct 13, 2016

### NuclearBoofluff

But that's just circular reasoning. Of course it's going to increase in energy (I thought it was potential) as it goes up. But what is the underlying mechanics behind these rules? Why is a full shell defined as a full shell; and what makes moving up an orbital/energy level so energy consuming?

4. Oct 14, 2016

### DrDu

The orbitals also of complex atoms are similar to the orbitals in the hydrogen atom. There you find that the orbitals have energies proportional to $-1/n^2$, where n-1 is the number of nodal planes of the orbitals. This is to be expected from the wavefunctions being standing waves. The kinetic energy of standing waves increases the higher the number of nodes. In the Coulombic potential of the nucleus, this effect is partially compensated by the orbitals with more nodes becoming more extended, which however increases their potential energy. Anyhow, the quantum number n is known as the principal quantum number which defines the shell. Now due to the Pauli exclusion principle, each orbital can hold at most 2 electrons (with anti-parallel spin). There are $n^2$ orbitals for each shell n, so each shell can hold at most $2n^2$ electrons. This defines what is meant by a full shell. E.g. in He, n=1 and He has 2 electrons, in Ne, the maximal n=2 and Ne has two full shells, the one with n=1, holding 2 electrons and the one with n=2 holding 8 electrons. Any additional electron would have to go to the next shell, with much higher energy.