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GATE 2021 PH – Question 42

Nuclear and Particle Physics · Liquid drop model, nuclear shell model · 2 marks · Multiple choice

The two sets of nuclear energy levels are shown. Nuclei X and Y have odd and even mass numbers, respectively. Choose the best interpretation.

Diagram for GATE 2021 PH question 42
  1. Set I: rotational band of X; Set II: vibrational band of Y.
  2. Set I: rotational band of Y; Set II: vibrational band of X.
  3. Set I: vibrational band of X; Set II: rotational band of Y.
  4. Set I: vibrational band of Y; Set II: rotational band of X.

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Show answer and explanation

Correct answer: (D) Set I: vibrational band of Y; Set II: rotational band of X.

Explanation

Set I has a $0^+$ ground state, a $2^+$ state at 600 keV and a $0^+,2^+,4^+$ multiplet at 1200 keV. These are the zero-, one- and two-phonon pattern of a quadrupole vibrator in an even-mass nucleus, so it belongs to Y. Set II has half-integer spins $7/2,11/2,15/2,19/2,23/2$ whose energies follow rotational $J(J+1)$ spacings above a band head; it belongs to odd-mass X. Thus D.

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