You can do it like this:
The effective nuclear charge
We can calculate
Electrons are grouped together in increasing order of
You can calculate the screening constant as follows:
Add 0.35 for each other electron within the same group, except for
If the group is of the
Lets apply this to
The electron structure is:
For a 3d electron:
Within the 3d group there are 4 other electrons giving 4 x 0.35 = 1.40 units.
There are 18 other electrons closer to the nucleus giving 18 x 1.00 =18.0 units.
For a 4s electron:
Within the 4s group there is 1 other electron giving 1 x 0.35 = 0.35 units.
In the (n - 1) group, which are the 3s, 3p and 3d, electrons there are 13 electrons giving 13 x 0.85 = 11.05 units
This leaves 10 (n - 2) electrons. This gives 10 x 1 = 10 units.
This shows that the 4s electrons experience a smaller effective nuclear charge than the 3d electrons so are more easily lost
This is consistent with observations.