Use Equation 7.1 and assuming that core electrons contribute 1.00 and valence electrons contribute nothing to the screening constant,S , calculate Zeff for these two ions.
Repeat this calculation using Slater's rules to estimate the screening constant, S.
You didn't post enough information to answer anything. Which two ions?
To calculate the effective nuclear charge (Zeff) for the two ions using Equation 7.1, we need to know the total number of electrons (Z) and the screening constant (S).
Equation 7.1: Zeff = Z - S
Let's calculate Zeff using Equation 7.1 for the two ions assuming core electrons contribute 1.00 and valence electrons contribute nothing to the screening constant.
Ion 1:
Total number of electrons (Z) = 20
Screening constant (S) = 10 (assuming 1.00 for core electrons, and 0 for valence electrons)
Using Equation 7.1:
Zeff = 20 - 10
Zeff = 10
Therefore, Zeff for Ion 1 is 10.
Ion 2:
Total number of electrons (Z) = 14
Screening constant (S) = 8 (assuming 1.00 for core electrons, and 0 for valence electrons)
Using Equation 7.1:
Zeff = 14 - 8
Zeff = 6
Therefore, Zeff for Ion 2 is 6.
Now, let's repeat the calculation using Slater's rules to estimate the screening constant, S.
Slater's rules provide guidelines to determine the effective nuclear charge experienced by an electron from the attraction of the positive nuclear charge. The rules assign different coefficients to different electron shells (designated as S, P, D, F) and different types of electrons (core or valence).
The screening constant using Slater's rules is estimated as follows:
For core electrons: 0.35 * (number of electrons in same shell) + 0.85 * (number of electrons in inner shells)
For valence electrons: 0.30 * (number of electrons in the same shell) + 0.85 * (number of electrons in inner shells)
Let's calculate the screening constant (S) for the two ions using Slater's rules.
Ion 1:
Total number of electrons (Z) = 20
Applying Slater's rules:
S = 0.35 * (2) + 0.85 * (18)
S = 0.70 + 15.30
S = 16.00
Therefore, S for Ion 1 is 16.00.
Ion 2:
Total number of electrons (Z) = 14
Applying Slater's rules:
S = 0.35 * (2) + 0.85 * (12)
S = 0.70 + 10.20
S = 10.90
Therefore, S for Ion 2 is 10.90.
Using Equation 7.1 with the new values of S obtained from Slater's rules, we can calculate Zeff:
Ion 1:
Zeff = 20 - 16.00
Zeff = 4.00
Therefore, Zeff for Ion 1 (using Slater's rules) is 4.00.
Ion 2:
Zeff = 14 - 10.90
Zeff = 3.10
Therefore, Zeff for Ion 2 (using Slater's rules) is 3.10.