The quantum number representing the ground state of gadolinium is 9D2.
Understanding Atomic Quantum Numbers
In atomic physics, the quantum state of an atom is often described by a term symbol, which is a concise notation summarizing the total angular momenta of all electrons in the atom. This symbol, typically written as ${}^{2S+1}L_J$, provides crucial information about the atom's electronic configuration and its energetic state. It accounts for the total spin angular momentum (S), total orbital angular momentum (L), and the total angular momentum (J) of the atom.
Gadolinium's Ground State Term Symbol
For gadolinium (Gd), a rare-earth element, its ground state is characterized by the term symbol 9D2. Breaking down this specific symbol:
- 9 (Superscript): This represents the spin multiplicity, calculated as $2S+1$. A multiplicity of 9 indicates that the total spin angular momentum (S) is 4. This signifies a high degree of unpaired electron spins, common in lanthanides.
- D (Letter): This letter corresponds to the total orbital angular momentum (L). In spectroscopic notation, L=0 is S, L=1 is P, L=2 is D, L=3 is F, and so on. Therefore, 'D' indicates that the total orbital angular momentum (L) for gadolinium in its ground state is 2.
- 2 (Subscript): This is the total angular momentum (J), which arises from the coupling of the total spin (S) and total orbital (L) angular momenta. For gadolinium, the total angular momentum J is 2.
This unique combination of S, L, and J values defines the precise quantum state of the gadolinium atom in its most stable, lowest energy configuration.
The following table summarizes the key quantum information for gadolinium:
| Element | Ground State Term Symbol |
|---|---|
| Gadolinium | 9D2 |
