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Here are the term symbols for the given electron configurations and explanations:
a. s1
Electron Configuration: One electron in an s orbital.
L (Orbital Angular Momentum): The s orbital has l = 0, so L = 0.
S (Spin Angular Momentum): One electron has spin s = 1/2. Since there's only one electron, the total spin S = 1/2.
J (Total Angular Momentum): J = |L + S| to |L - S| = 1/2.
Term Symbol: ²S1/2
b. p1
Electron Configuration: One electron in a p orbital.
L (Orbital Angular Momentum): The p orbital has l = 1, so L = 1.
S (Spin Angular Momentum): One electron has spin s = 1/2, so S = 1/2.
J (Total Angular Momentum): J = |L + S| to |L - S| = 3/2, 1/2.
Term Symbol: ²P3/2, ²P1/2
c. s1p1
Electron Configuration: One electron in an s orbital and one in a p orbital.
L (Orbital Angular Momentum): L = |l1 + l2| to |l1 - l2| = 1 (since l1 = 0 for s and l2 = 1 for p).
S (Spin Angular Momentum): Two electrons, each with spin s = 1/2. S can be 0 (antiparallel spins) or 1 (parallel spins).
J (Total Angular Momentum):
For S = 0: J = L = 1, giving the term symbol ¹P1
For S = 1: J = 0, 1, 2, giving the term symbols ³P0, ³P1, ³P2
Explanation of Term Symbols:
Multiplicity: The superscript before the letter indicates the multiplicity, which is 2S + 1. This represents the number of possible spin states. For example, ² means 2(1/2) + 1 = 2, which is a doublet state.
L (Orbital Angular Momentum): The letter represents the value of L: S (L = 0), P (L = 1), D (L = 2), F (L = 3), etc.
J (Total Angular Momentum): The subscript represents the value of J.