Question

Based on crystal field theory, which of the following metal ions will not be colored when placed in an octahedral crystal field?

Au+
Fe3+
Ag+
Au3+
Nb3+

Answer 1

Look up the electron configuration for the element (if you don't have that in your text you can go to www.webelemets.com and click on the element, then scroll down on the left side to electron shell properties to obtain them). I'll do the first one.
Au is [Xe]4f14 5d10 6s1; therefore, the Au^+ must have the 6s1 electron removed and it will be [Xe]4f14 5d10. None of the electrons is unpaired and when split in a field all still will be paired; therefore, no color.
The Au^3+ ion is
[Xe]4f14 5d8.
......e_g......t_2g
.....><..><..>............>..>
(Note: < is for spin of the electron up and < is for the opposite.)
There will be unpaired electrons; therefore, Au^3+ salts should be colored.

You do the others the same way.

Answer 2

Two problems. The spacing is not done very well and I interchanged the e_g and t_2g. I'll try again.
.....t_2g......e_g
.....><..><..>...................>..>

Answer 3

.....t_2g.............
.....><..><..>......<..<

Answer 4

.....t_2g.........e_g
.....><..><..>.......>..>

Answer 5

Just move the e_g heading to the right so the two unpaired electrons are under that column.