For the following pairs of atoms, calculate the effective nuclear charge. Indica

Question

For the following pairs of atoms, calculate the effective nuclear charge. Indicate which of the pair has the largest radius, which has the larger ionization energy. a. F vs. S Zeff = __________________ Larger radius = _______________; larger ionization energy___________ b. Be vs. Mg Zeff = __________________ Larger radius = _______________; larger ionization energy___________ c. As vs. Br Zeff = __________________ Larger radius = _______________; larger ionization energy___________

2. For the following pairs of atoms or ions, calculate the effective nuclear charge. Indicate which of the pair has the largest radius, which has the larger electron affinity. a. N vs. F Zeff = __________________ Larger radius = _______________; larger ionization energy___________ b. Li vs. K Zeff = __________________ Larger radius = _______________; larger ionization energy___________ c. P vs. Se Zeff = __________________ Larger radius = _______________; larger ionization energy___________

3. Which of the following is NOT isoelectronic with S2-? P3- , Ar, F-, Cl-, K+ Of those in the listing that ARE isoelectronic, arrange them in order of increasing radius.

Explanation / Answer

I will answer only question 1 and explain to you how to calculate the effective nuclear charge, so you can do question 2. The radius and electron afinity you can see in a periodic table and compare:

To calculate the effective nuclear charge, you need to use the following equation:

Z* = Z - s

Z: atomic number

s: number of electrons between the nucleus and the electron (shield effect)

The value of s, can be calculated in this way:

1. Write down the electronic configuration of the element

2. Any electrons to the right of the electron of interest do not contribute to shielding constant.

3. The shielding constant for each group is formed as the sum of the following contributions:

All other electrons in the same group as the electron of interest shield to an extent of 0.35 nuclear charge units except 1s group, where the other electron contributes only 0.30.

If the group is of the [s, p] type, an amount of 0.85 from each electron (n-1) shell and an amount of 1.00 for each electron from (n-2) and lower shell.

If the group is of the [d] or [f] type then an amount of 1.00 for each electron from all lying left to that orbital.

Following this rules, let's calculate Z* for every case:

a) [F] = 1s2 2s2 2p5 ----> s = (7x0.35) + (0.85x2) = 4.15 ; Z* = 9 - 4.15 = 4.85

[S] = 1s2 2s2 2p6 3s2 3p4 -----> s = (6x0.35) + (8x0.85) + 2x1 = 10.9; Z* = 16 - 10.9 = 5.1

Larger Z*: S

Larger radius: S (Atomic radius = 1.27 A) (F atomic radius: does not have)

Larger ionization energy: F with 17.42 eV while S has 10.32 eV

b) [Be] = 1s2 2s2 ----> s = 2x0.35 + 2x0.85 = 2.4; Z* = 4 - 2.4 = 1.6

[Mg] = 1s2 2s2 2p6 3s2 ---> s = 2x0.35 + 8x0.85 + 2x1 = 9.5; Z* = 12 - 9.5 = 2.5

Larger Z*: Be

Larger radius: Mg with 1.72 A (Be has 1.4 A)

Larger ionization energy: Be with 9.32 (Mg has 7.65)

c) [As] = 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p3 ---> s = 5x0.35 + 8x0.85 + 20x1 = 28.55; Z* = 33 - 28.55 = 4.45

[Br] = 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p5 ----> s = 7x0.35 + 8x0.85 + 20x1 = 29.25; Z* = 35 - 29.25 = 5.75

Larger Z*: Br

Larger radius: As with 1.33 A (Br has 1.12)

Larger ionization energy: Br with 11.88 eV (As has 9.78 eV)

You can do the same thing with the atoms of question 2. If you have doubts or question, you may tell me in a comment.

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