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Mn3+ ion has four 3d electrons. The spectroscopic term factor of this ion is :

  • A.\({}^{1}D_{2}\)
  • B.\({}^{4}F_{3/2}\)
  • C.\({}^{3}F_{9/2}\)
  • D.\({}^{5}D_{0}\)

Answer: D

The ground term is \({}^{5}D_{0}\).

Apply Hund's rules to \(3d^{4}\):

  • Maximum S: four parallel spins, \(S = 2\), multiplicity \(2S + 1 = 5\).
  • Maximum L for that S: \(m_{l} = 2, 1, 0, -1\), so \(L = 2\), a D term.
  • The shell is less than half full, so \(J = |L - S| = 0\).

The term is \({}^{5}D_{0}\). \({}^{1}D_{2}\) has the wrong spin, and the terms with half-integer J require an odd number of electrons.

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