Question
The number of microstates in term $^{1}G$ is ______________
To find the number of microstates in the term $^{1}G$, we need to recall the rules for determining microstates for a given term symbol. A term symbol is given by $^{2S+1}L_J$, where $S$ is the total spin quantum number, $L$ is the total orbital angular momentum, and $J$ is the total angular momentum.
In the term $^{1}G$, the superscript '1' signifies that the multiplicity $2S+1=1$, which implies $S=0$. The letter 'G' represents the orbital angular momentum quantum number, with $L$ values assigned as follows: S=0, P=1, D=2, F=3, G=4, etc. Thus, for $G$, $L=4$.
The number of microstates is given by $(2L+1)(2S+1)$. For the term $^{1}G$:
- $2S+1=1$ (since it is a singlet state)
- $2L+1=9$ (with $L=4$).
Therefore, the total number of microstates is $1 \times 9 = 9$. This result is consistent with the expected range of (9, 9).
Thus, the number of microstates in term $^{1}G$ is 9.
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