Use Slater's rules to calculate the effective nuclear charge, Z* or Zeff, for a 4f electron in Eu, Tb, and Dy.
To calculate the effective nuclear charge (Z*) for a 4f electron in Eu (Europium), Tb (Terbium), and Dy (Dysprosium) using Slater's rules, we need to follow these steps:
1. Write out the electron configuration for the atom in question.
The electron configurations for Eu, Tb, and Dy are as follows:
Eu: [Xe] 4f^7 6s^2
Tb: [Xe] 4f^9 6s^2
Dy: [Xe] 4f^10 6s^2
2. Assign the shielding constants for each electron group.
The shielding constants for the different electron groups are as follows:
For the 1s^2 electron pair: σ = 0.30
For the 2s^2 and 2p^6 electron pairs: σ = 0.85
For the 3s^2 and 3p^6 electron pairs: σ = 1.00
For the 3d^10 electron pair: σ = 0.35
For the 4s^2 and 4p^6 electron pairs: σ = 1.00
For the 4d^10 electron pair: σ = 0.35
For the 5s^2 and 5p^6 electron pairs: σ = 1.00
For the 5d^10 electron pair: σ = 0.35
3. Apply the Slater's rules to calculate the effective nuclear charge (Z*) for the 4f electron.
According to Slater's rules,
Z* = Z - S
where Z is the nuclear charge and S is the shielding constant.
For Eu:
Z* = 63 - (7 * 0.35 + 8 * 1.00) = 63 - (2.45 + 8) = 63 - 10.45 = 52.55
For Tb:
Z* = 65 - (9 * 0.35 + 8 * 1.00) = 65 - (3.15 + 8) = 65 - 11.15 = 53.85
For Dy:
Z* = 66 - (10 * 0.35 + 8 * 1.00) = 66 - (3.50 + 8) = 66 - 11.50 = 54.50
Therefore, the effective nuclear charge (Z*) for a 4f electron in Eu is approximately 52.55, in Tb is approximately 53.85, and in Dy is approximately 54.50.
To calculate the effective nuclear charge (Z*) for a 4f electron in Eu, Tb, and Dy using Slater's rules, follow these steps:
Step 1: Write down the electron configuration for the element.
Eu: [Xe] 4f^7 6s^2
Tb: [Xe] 4f^9 6s^2
Dy: [Xe] 4f^10 6s^2
Step 2: Assign shielding values to each electron group based on the following rules:
- For electrons in the same group as the one being considered, assign a shielding value of 0.35.
- For electrons in the next inner group, assign a shielding value of 0.85.
- For all remaining electrons, assign a shielding value of 1.
Step 3: Apply Slater's rules to calculate the effective nuclear charge.
a) For Eu (Z = 63):
- For the 4f electrons, there are 7 electrons in the same group, so the total shielding contribution is 7 x 0.35 = 2.45.
- For the 6s electrons, there are 2 electrons in the next inner group, so the total shielding contribution is 2 x 0.85 = 1.70.
Z* for the 4f electron in Eu = Z - total shielding contribution = 63 - (2.45 + 1.70) ≈ 58.85.
b) For Tb (Z = 65):
- For the 4f electrons, there are 7 electrons in the same group, so the total shielding contribution is 7 x 0.35 = 2.45.
- For the 6s electrons, there are 2 electrons in the next inner group, so the total shielding contribution is 2 x 0.85 = 1.70.
Z* for the 4f electron in Tb = Z - total shielding contribution = 65 - (2.45 + 1.70) ≈ 60.85.
c) For Dy (Z = 66):
- For the 4f electrons, there are 9 electrons in the same group, so the total shielding contribution is 9 x 0.35 = 3.15.
- For the 6s electrons, there are 2 electrons in the next inner group, so the total shielding contribution is 2 x 0.85 = 1.70.
Z* for the 4f electron in Dy = Z - total shielding contribution = 66 - (3.15 + 1.70) ≈ 61.15.
So, the effective nuclear charge (Z*) for a 4f electron in Eu is approximately 58.85, in Tb is approximately 60.85, and in Dy is approximately 61.15.
I may have missed something here but it appears this site has all of the rules. It may be painstaking to apply the rules but I don't think I need to do it for you.
http://en.wikipedia.org/wiki/Slater%27s_rules