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. Express your answers as integers. Enter your answers numerically separated by a comma.
Equation 7.1: Zeff=Z-S
Zeff Cl-, Zeff K+
To calculate Zeff for Cl- and K+ using Equation 7.1, we need to determine the screening constant, S.
For Cl-:
Since Cl has 17 electrons, including 10 core electrons (1s^2 2s^2 2p^6), we assume that these core electrons contribute a value of 1.00 to the screening constant. The valence electrons (3s^2 3p^5) contribute nothing to the screening constant.
So, for Cl-:
Zeff = Z - S
Zeff = 17 - 1.00
Zeff = 16
For K+:
Since K has 19 electrons, including 10 core electrons (1s^2 2s^2 2p^6 3s^2 3p^6), we assume that these core electrons contribute a value of 1.00 to the screening constant. The valence electron (4s^1) contributes nothing to the screening constant.
So, for K+:
Zeff = Z - S
Zeff = 19 - 1.00
Zeff = 18
Therefore, the values of Zeff for Cl- and K+ are 16 and 18, respectively.
To calculate Zeff using Equation 7.1, we need to determine the value of S first. In this case, assuming that core electrons contribute 1.00 to the screening constant and valence electrons contribute nothing, the value of S can be determined by counting the number of core electrons.
1. For Zeff Cl-, we will calculate S for this ion:
Cl has 17 electrons. To determine the number of core electrons, we need to subtract the valence electrons. Chlorine is in Group 17, so it has 7 valence electrons.
Number of core electrons = Total number of electrons - Valence electrons
Number of core electrons = 17 - 7
Number of core electrons = 10
Since core electrons contribute 1.00 to the screening constant, S = 1.00 for Cl-.
Now we can substitute the values into Equation 7.1:
Zeff Cl- = Z - S
Zeff Cl- = 17 - 1.00
Zeff Cl- = 16
Therefore, Zeff Cl- = 16.
2. For Zeff K+, we will calculate S for this ion:
K has 19 electrons, and since it is in Group 1, it has 1 valence electron.
Number of core electrons = Total number of electrons - Valence electrons
Number of core electrons = 19 - 1
Number of core electrons = 18
Since valence electrons contribute nothing to the screening constant, S = 0.00 for K+.
Now we can substitute the values into Equation 7.1:
Zeff K+ = Z - S
Zeff K+ = 19 - 0.00
Zeff K+ = 19
Therefore, Zeff K+ = 19.
In summary:
Zeff Cl- = 16
Zeff K+ = 19
Cl- => Atomic number 17 - 10 (Core electrons from [Ne] = 7
K+ => Atomic Number 19 - 18 (Core electrons fom [Ar] = 1