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Chapter 26: Problem 3

Determine the ground-state term for the following free gaseous atoms: (a) \(\mathrm{C}\) (b) \(\mathrm{N}\) (c) Ca (d) Co (e) \(\mathrm{Zn}\)

Short Answer

Expert verified
The ground-state terms for the atoms will be: (a) Carbon (C): \(^3P\), (b) Nitrogen (N): \(^4S\), (c) Calcium (Ca): \(^1S\), (d) Cobalt (Co): \(^4F\), and (e) Zinc (Zn): \(^1S\).

Step by step solution

01

Obtain the Electron Configuration

Obtain the electron configuration of each atom using the periodic table. For example, the electron configuration of Carbon (C) is 1s2 2s2 2p2.
02

Label the Configuration

Label each configuration according to the spectroscopic notation. Carbon (C) is in the P block of the periodic table hence it's a P type atom: \(^{2}P\).
03

Follow Hund's Rules

Hund's rules state that for a given electron configuration, the term with maximum multiplicity has the lowest energy. The term symbol is represented as \(\ ^{2S+1}L_J\), where \(L\) takes values from integers assigned to the spectral sequence S, P, D.... When we apply this to Carbon, we get: \( ^3P_0, ^3P_1, ^3P_2\)
04

Repeat for Other Atoms

Repeat these steps for the other atoms given: Nitrogen (N), Calcium (Ca), Cobalt (Co), and Zinc (Zn). Then derive the term symbols accordingly.

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Most popular questions from this chapter

Discuss quenching of orbital momentum in detail.

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Give reasons for the following: (a) \(\left[\mathrm{Mn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) is pale coloured. (b) Anhydrous \(\mathrm{CuSO}_{4}\) is white but \(\mathrm{CuSO}_{A} .5 \mathrm{H}_{2} \mathrm{O}\) is blue in colour.

Determine the \(\Delta_{0}\) values for \(\left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) and \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) if \(0\left({ }^{3} A_{2 g} \rightarrow{ }^{3} T_{2 g}\right)\) is \(8700 \mathrm{~cm}^{-1}\) and \(\cup\left({ }^{4} T_{1 g} \rightarrow{ }^{4} T_{2 g}\right)\) is \(8000 \mathrm{~cm}^{-1}\). Also draw Orgel diagrams for these complexes.

What is the difference between \(L-S\) coupling and \(j-j\) coupling? Discuss the significance of both schemes.
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