Here's a video explanation of Slater's Rules (11min): Using Slater's Rules, by chemistNATE, on YouTube
Effective nuclear charge is really important, because it determines the size and energy of orbitals, which determine most properties of atoms. So it's useful to be able to predict effective nuclear charge! Slater's rules give a simple approximation of effective nuclear charge that works pretty well.
Based on the last section, we can expect that effective nuclear
charge will depend on the number of electrons that might get
between, so it depends on the electron we are looking at. For any
electron, to find the effective nuclear charge it feels, we need to
know how many other electrons might get in the way, and how much
time it spends near the nucleus. Based on these, we will calculate a
shielding constant, S. Then,
Zeff = Z - S
where Z is the actual nuclear charge (which is the same as the atomic number) and Zeff is the
effective nuclear charge.
To calculate S, we will write out all the electrons in atom until
we get to the group of the electron we want, like this:
(1s)(2s,2p)(3s,3p)(3d)(4s,4p)(4d)(4f)(5s,5p) etc.
The outcome of this is that Zeff changes suddenly when going from one period to another. As you go from Li to Be, Zeff (for the new electron) increases, because you add one proton (Z + 1) and it is only shielded 35% (S + 0.35). When you get to B, you added one proton, and it still shields 35%. So Zeff increases until you go from Ne to Na. Now, suddenly, the (1s) electrons shield 100% instead of 85%, and the (2s,2p) shield 85% instead of 35%! So Zeff goes down suddenly. From Na to Ar, Zeff increases slowly again. From Ar to K, it drops again.
For an example, let's calcalate Zeff for a d electron
in Zn, atomic number 30. Notice that although 4s is filled, we don't
include it because it comes to the right of the d electrons we are
looking at.
(1s)(2s,2p)(3s,3p)(3d)
S = 18(1) + 9(0.35) = 21.15
Zeff = 30 - 21.15 = 8.85
For another example, we'll calculate for the p electron in Ga,
atomic number 31.
(1s)(2s,2p)(3s,3p)(3d)(4s,4p)
S = 10(1) + 18(0.85) + 2(0.35) = 26.00
Zeff = 31 - 26 = 5
You can see that just like changing periods (going to a new shell),
going from the d-block to the p-block also gives a drop in
Zeff (partly because you actually are going to a new
shell, as well as subshell).