Part A: Calculate Zeff for a valence electron in a...

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Part A: Calculate Zeff for a valence electron in an oxygen atom.Part B: Calculate Zeff for the 4s electron in a copper atom, Cu.Part C: Calculate Zeff for a 3d electron in a copper atom, Cu.

Jules Bruno · Accepted Answer

Part A:We’re being asked to calculate the effective nuclear charge (Zeff) of the valence electron in oxygen (O) atom. Recall that the effective nuclear charge is the forces exerted by the nucleus onto an electron and is given by:where Z = nuclear charge or atomic number and S = shielding constant. For this problem, we need to do the following steps:Step 1: Determine the atomic number.Step 2: Determine the electron configuration and group them by n-values.Step 3: Calculate for the shielding constant.Step 4: Calculate for Zeff.[readmore]Step 1: The atomic number of O is 8.Step 2: The location of O in the periodic table is shown below:Based on the figure, O belongs in the p-block in Group 6A and Period 2 so its electron configuration will contain the 1s, 2s and 2p subshells. Recall that: • s–subshell can hold a maximum of 2 electrons• p–subshell can hold a maximum of 6 electronsSince O is neutral, it has 8 electrons. Starting from 1s, the electron configuration for O is: 1s22s22p4The valence electrons are found in the outermost shell. For O, the outermost shell is n = 2. Grouping this by n-value gives us:(1s2)(2s2, 2p4)Step 3: There are 6 valence electrons. Each of the valence electrons is shielded by the other 5 electrons. Moreover, all of the other electrons to the left of (2s2, 2p4) are shielding it. The shielding constant can be calculated using Slater’s Rules:For ns and np electrons:1. Each electron in the same group will contribute 0.35 to the S value. A 1s electron contributes 0.30 to the S value of another 1s electron.2. Each electron in the n–1 group contributes 0.85 to the S value.3. Each electron in the n–2 or greater group contributes 1.00 to the S value.This means for an electron in (2s, 2p):1. There are 5 other electrons in the group (2s, 2p) (S contribution is 5 × 0.35 = 1.75)2. 1s are n–1 group with a total of 2 electrons. This means the contribution to the S value is 2 × 0.85 = 1.70The total S value is 1.75 + 1.70 = 3.45Step 4: Calculating for Zeff: 8 – 3.45 = 4.55The effective nuclear charge for a valence electron in O is 4.55Part B:Step 1: The atomic number of Cu is 29.Step 2: The location of Cu in the periodic table is shown below:Based on the figure, Cu belongs in the d-block in Period 4 so its electron configuration will contain the 4s and 3d subshells. Recall that: • s–subshell can hold a maximum of 2 electrons• p–subshell can hold a maximum of 6 electrons• d–subshell can hold a maximum of 10 electronsSince Cu is neutral, it has 29 electrons. Starting from 1s, the electron configuration for Cu is: 1s22s22p63s23p64s23d9Recall that subshells prefer to be completely- or half-filled. This means we can move an electron from the 4s subshell to a 3d subshell to get a more stable configuration:1s22s22p63s23p64s13d10Grouping this by n-value gives us:(1s2)(2s2, 2p6)(3s2, 3p6)(3d10)(4s1)Step 3: Since there’s only 1 electron in the 4s orbital, all of the other electrons to the left of 4s are shielding it. The shielding constant can be calculated using Slater’s Rules:For ns and np electrons:1. Each electron in the same group will contribute 0.35 to the S value. A 1s electron contributes 0.30 to the S value of another 1s electron.2. Each electron in the n–1 group contributes 0.85 to the S value.3. Each electron in the n–2 or greater group contributes 1.00 to the S value.For nd and nf electrons:1. Each electron in the same group will contribute 0.35 to the S value.2. Each electron in the groups to the left contributes 1.00 to the S value.This means for an electron in the 4s orbital:1. There are no other electrons in the same group as 4s (S contribution is 0 × 0.35 = 0)2. 3s, 3p, and 3d are n–1 groups with a total of 18 electrons. This means the contribution to the S value is 18 × 0.85 = 15.33. 1s, 2s, and 2p are n–2 or greater groups with a total of 10 electrons. This means the contribution to the S value is 10 × 1.00 = 10The total S value is 15.3 + 10 = 25.3Step 4: Calculating for Zeff: 29 – 25.3 = 3.7The effective nuclear charge for a 4s electron in Cu is 3.7.Part C:Considering a 3d electron is a copper Cu atom:Grouping by n-value gives us:(1s2)(2s2, 2p6)(3s2, 3p6)(3d10)(4s1)Step 3: There are 10 3d electrons. Each of the electrons is shielded by the other 9 electrons in the same group. Moreover, all of the other electrons to the left of (2s2, 2p4) are shielding it. The shielding constant can be calculated using Slater’s Rules*Note: Electrons to the right of the group are not considered because they do not shield the inner electronsThis means for an electron in the 3d orbital:1. There are 9 other electrons in the same group as 3d (S contribution is 9 × 0.35 = 3.15)2. 3s, and 3p, are n–1 groups with a total of 8 electrons. This means the contribution to the S value is 8 × 0.85 = 6.83. 1s, 2s, and 2p are n–2 or greater groups with a total of 10 electrons. This means the contribution to the S value is 10 × 1.00 = 10The total S value is 3.15 + 6.8 + 10 = 19.95Step 4: Calculating for Zeff: 29 – 19.05 = 9.05The effective nuclear charge for a 3d electron in Cu is 9.05.

Problem: Part A: Calculate Zeff for a valence electron in an oxygen atom.Part B: Calculate Zeff for the 4s electron in a copper atom, Cu.Part C: Calculate Zeff for a 3d electron in a copper atom, Cu.

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Problem: Part A: Calculate Zeff for a valence electron in an oxygen atom.Part B: Calculate Zeff for the 4s electron in a copper atom, Cu.Part C: Calculate Zeff for a 3d electron in a copper atom, Cu.

FREE Expert Solution

Problem Details

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