The way that I learned how to calculate effective nuclear charge was using Slater's Rules, which say...well a lot of stuff:

**Slater's Rules**Z* = Z - S

Z* = Effective Nuclear Charge

Z = Actual Nuclear Charge

S = Shielding Factor

(Basically, Slater's Rules guide you through calculating S, the Shielding factor. Just follow these steps.)

1. Write the electron configuration for the atom using the following design:

(1s

^{2}) (2s

^{2}, 2p

^{6}) (3s

^{2}, 3p

^{6}) (3d

^{10}) (4s

^{2}, 4p

^{6}) (4d

^{10}) (4f

^{14}) (5s

^{2}, 5p

^{6}) (Note: the parentheses indicate those in the same group)

2.Any electrons to the right of the electron of interest contribute no shielding (and are therefore negligible in this calculation).

3.All other electrons in the same group as the electron of interest shield to an extent of 0.35 nuclear charge units, except for 1s where the value is 0.30. (Notice that it says all other electrons in the same group, so not counting the electron of interest)

4.

**If the electron is an s or p electron**, all electrons with a principle quantum number of n-1 shield to an extent of 0.85 units of nuclear charge. All electrons with a principle quantum number of n-2 or lower shield to an extent of 1.00 units.

5.

**If the electron of interest is a d or f electron**, all electrons to the left shield to an extent of 1.00 units of nuclear charge

6. Sum the shielding amounts from steps 3-5 and subtract from the actual nuclear charge value to obtain the effective nuclear charge.

Sorry, that's a lot of information. I'll run through one of your problems just to make sure you understand.

1. Calculate Z eff for a valence electron in an oxygen atom.

So, we're going to use the equation Z* = Z - S

Z, the actual nuclear charge, is always going to be equal to the number of protons in the nucleus of the atom. So in this case, the number of protons in an oxygen atom is 8, so Z = 8.

Now we use Slater's Rules to calculate the shielding factor.

So we set up the electron configuration. (1s

^{2}) (2s

^{2}, 2p

^{4}) (Since all electrons to the right of the one in interest are negligible, I only wrote 2p

^{4} instead of 2p

^{6})

Now we follow step 3 of Slater's Rules. So all

other electrons in the same group of the electron of interest shield 0.35. This means we take the number of electrons in that group and subtract 1 (since it is all of the electrons but the one of interest) and multiply that number by 0.35.

So there are 6 total electrons in our group. 6-1 is 5. 5 x 0.35 is

**1.75** nuclear charge units.

Next, we deal with the electrons in the other remaining groups (there's only one group left in problem, the 1s

^{2} group). So, step 4 says that the electrons in this group, since our electron is in an s or p group and since it has a principle quantum number of n-1, shield to an extent of 0.85 nuclear charge units.

So there are 2 total electrons here, and we don't need to subtract electrons anymore. 2 x 0.85 is

**1.7** nuclear charge units.

Now we can calculate Z* (effective nuclear charge). First we follow step six and sum up our values.

**1.75 + 1.7 = 3.45** nuclear charge units.

Now we can follow the formula.

Z* = Z - S, so

**Z* = 8 - 3.45 = 4.55 nuclear charge units**.

I really hope that this helps you. I'll let you figure out the other two problems on your own.

-Xylofunk-