Consider the ground state electron configuration of titanium, Ti: [Ar] 4s2 3d2.ÂÂ
The total orbital angular momentum, L, for the ground state of Ti is _ and is represented by the letter ?
The total spin angular momentum, S, for the ground state of Ti is __ ?
The multiplicity, 2S+1, for the ground state of Ti is _ which is a _______?
The total angular momentum, J, of Ti can have the following possible values when L and S are determined from the ground state electron configuration.
The actual ground state term symbol for Ti has a J value of _?
The Correct Answer and Explanation is :
To determine the required properties for titanium (Ti\text{Ti}), consider its ground state electron configuration:
Electron configuration:
[Ar] 4s2 3d2[\text{Ar}] \, 4s^2 \, 3d^2
Titanium has two unpaired electrons in the 3d3d-orbital. Let’s calculate each property step by step:
1. Total Orbital Angular Momentum (LL):
- Each dd-electron has l=2l = 2 (orbital angular momentum quantum number). The possible mlm_l values are −2,−1,0,+1,+2-2, -1, 0, +1, +2.
- For two dd-electrons, we sum their mlm_l values:
- Maximum L=2+2=4L = 2 + 2 = 4, and we reduce LL using electron pairing rules (Hund’s rules). The two electrons are unpaired and occupy different mlm_l values to minimize repulsion. The resulting L=3L = 3 (corresponding to FF).
Answer: L=3L = 3, represented by FF.
2. Total Spin Angular Momentum (SS):
- Each electron has spin s=1/2s = 1/2. For two unpaired electrons:
- S=s1+s2=1/2+1/2=1S = s_1 + s_2 = 1/2 + 1/2 = 1 (maximum spin state due to parallel spins).
Answer: S=1S = 1.
3. Multiplicity (2S+12S+1):
- The multiplicity is given by 2S+12S + 1:
- 2(1)+1=32(1) + 1 = 3, corresponding to a triplet state.
Answer: Multiplicity = 33, which is a triplet.
4. Total Angular Momentum (JJ):
- The total angular momentum is J=∣L−S∣J = |L – S| to L+SL + S:
- Possible JJ values: ∣3−1∣,3,3+1|3 – 1|, 3, 3 + 1 → J=2,3,4J = 2, 3, 4.
The actual ground state follows Hund’s rules:
- Maximize JJ for less-than-half-filled subshells.
- Answer: J=2J = 2.
Ground State Term Symbol:
The ground state term symbol combines L,S,L, S, and JJ:
\text{Term Symbol: } \, ^3F_2