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GATE 2020 PH – Question 17

Nuclear and Particle Physics · Liquid drop model, nuclear shell model · 1 mark · Multiple choice

The total angular momentum j of the ground state of $^{17}_{8}\mathrm O$ is

  1. $1/2$
  2. 1
  3. $3/2$
  4. $5/2$

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Correct answer: (D) $5/2$

Explanation

$^{16}$O is a closed proton and neutron shell. The seventeenth nucleon in $^{17}$O is an unpaired neutron in the $1d_{5/2}$ orbital. Its orbital angular momentum is l = 2, coupled with spin 1/2 to the lower-energy j = 5/2 shell-model state. The closed core contributes zero, so ground-state j is 5/2, D.

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