For the d3 electron configuration, the ground state term symbol is
To find the ground state term symbol for an electron configuration like d3, we need to use Hund's rules. These rules help us determine the lowest energy state based on the total orbital angular momentum (L), total spin angular momentum (S), and total angular momentum (J).
Electron Configuration Analysis (d3)
The d subshell has 5 orbitals, corresponding to magnetic quantum numbers (ml) of +2, +1, 0, -1, and -2. Each orbital can hold a maximum of 2 electrons (one with spin +1/2 and one with spin -1/2).
For a d3 configuration, we have 3 electrons to place in these 5 orbitals. According to Hund's first rule, electrons will fill the orbitals singly with parallel spins as much as possible to maximize the total spin.
- Place the first electron in the highest ml orbital (+2) with spin up (+1/2).
- Place the second electron in the next highest ml orbital (+1) with spin up (+1/2).
- Place the third electron in the next highest ml orbital (0) with spin up (+1/2).
The electron arrangement looks like this:
- Electron 1: ml = +2, ms = +1/2
- Electron 2: ml = +1, ms = +1/2
- Electron 3: ml = 0, ms = +1/2
- Orbitals -1 and -2 are empty.
Orbital and Spin Angular Momentum (L and S)
Next, we calculate the total orbital angular momentum (L) and total spin angular momentum (S).
- Total L is the sum of the ml values for all electrons:
\(L = \sum m_l = (+2) + (+1) + (0) = +3\)
The value of L corresponds to a specific letter for the term symbol:
\(L=0 \rightarrow S\)
\(L=1 \rightarrow P\)
\(L=2 \rightarrow D\)
\(L=3 \rightarrow F\)
Since L = 3, the term symbol letter is F.
- Total S is the sum of the ms values for all electrons:
\(S = \sum m_s = (+1/2) + (+1/2) + (+1/2) = +3/2\)
The spin multiplicity is given by \(2S + 1\).
\(2S + 1 = 2(3/2) + 1 = 3 + 1 = 4\)
So far, the term symbol is $^{2S+1}$L = $^{4}$F.
Calculating Total Angular Momentum (J)
The total angular momentum (J) is determined by Hund's third rule. For subshells that are less than half-filled with electrons, \(J = |L - S|\). For subshells that are more than half-filled, \(J = L + S\). For exactly half-filled subshells, \(J = S\).
A d subshell can hold a maximum of 10 electrons. Thus, a half-filled d subshell has 5 electrons. The d3 configuration (3 electrons) is less than half-filled.
Therefore, we use the formula \(J = |L - S|\).
\(J = |3 - 3/2| = |6/2 - 3/2| = |3/2| = 3/2\)
Ground State Term Symbol
Combining the spin multiplicity ($2S+1=4$), the orbital angular momentum letter (F for L=3), and the total angular momentum (J=3/2), the ground state term symbol for the d3 electron configuration is $^{2S+1}$L$_J$ = $^{4}$F$_{3/2}$.
| Configuration | Number of electrons | Max electrons in subshell | Half-filled or less? | L | S | 2S+1 | J | Term Symbol |
|---|---|---|---|---|---|---|---|---|
| d3 | 3 | 10 | Less than half (3 < 5) | 3 (F) | 3/2 | 4 | |3 - 3/2| = 3/2 | $^{4}$F$_{3/2}$ |
This matches the term symbol $^{4}$F$_{3/2}$.
Important Questions from Term Symbol
The number of micro states corresponding to the atomic term symbol 4F is
The possible terms arising from a p1d1 configuration are
The ground state term symbol and the gj value for Pr3+ ion, respectively are (Atomic number of Pr is 59)
The term symbol for the ground dinitrogen cation radical (\(N^+_2\)) is
For the Eu3+ ion (At No: 63),
A. the calculated and the observed magnetic moments are in agreement with each other.
B. the higher energy states 7F1 and 7F2 are populated and increase the observed magnetic moment.
C. the 4f orbital is more than half-filled.
D. the ground state term symbol is 7F0.
Of the above, the correct statements are
