Question:medium

Find the ground state term symbol for Pr\(^{3+}\) (Pr = 59).

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For rare earth ions like Pr\(^{3+}\), the term symbol is derived from the \( 4f^n \) configuration and the values of \( S \) and \( L \).
Updated On: Feb 10, 2026
  • \( ^3H_4 \)
  • \( ^3H_6 \)
  • \( ^3H_5 \)
  • \( ^4F_{5/2} \)
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The Correct Option is C

Solution and Explanation

Step 1: Electronic Configuration of Pr\(^{3+}\).
Praseodymium (Pr) has atomic number 59. Its electronic configuration is: \[\text{Pr:} [Xe] 4f^3 6s^2\]Removing three electrons to form \( \text{Pr}^{3+} \) results in the configuration \( 4f^3 \).

Step 2: Term Symbol Calculation.
For \( 4f^3 \): the total spin quantum number (\( S \)) is 3/2, and the total orbital quantum number (\( L \)) is 3 (denoted as H). The multiplicity is \( 2S+1 = 2(3/2) + 1 = 4 \). Therefore, the term symbol is \( ^4H_5 \).

Step 3: Conclusion.
The ground state term symbol for Pr\(^{3+}\) is \( ^4H_5 \), corresponding to option (3).

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