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The 4f term with a d3 electron arrangement has a total of 10 microstates. This is because the 4f subshell can hold up to 14 electrons, and the d3 configuration allows for multiple ways to arrange the electrons in the f orbitals. Specifically, the d3 configuration has 3 electrons in the d orbitals, which can be distributed among the 5 d orbitals in 10 different ways. This is determined by the following equation:
Microstate = (n!)/(r!
(n-r)!)
Where n is the total number of orbitals (5 for d orbitals) and r is the number of electrons (3 for d3).
Therefore, (5!)/(3!
(5-3)!) = 10 microstates.