Unit 4 : Additional Problems

Unit 4 : Additional Problems#

For those looking for additional problems outside of past exam questions and the worked problems in the lectures please consider the following in the reading list.

  • What is the shell model of the nucleus, and how does it help determine the ground-state properties of nuclei?

  • How does the Pauli exclusion principle affect the arrangement of nucleons in nuclear shells?

  • What are magic numbers, and why are they significant in determining nuclear stability and structure?

  • How would you assign the spin of a nucleus for which the highest energy shell is one nucleon away from being full?

  • Give two reasons why the shell model energy levels for protons are slightly different than for neutrons.

  • What are the expected ground state spins and parities for the following nuclei Li-7, P-31, I-127?

  • How do you determine the total angular momentum (spin) of a nucleus using the shell model?

  • Why does the spin of a nucleus with an even number of protons and neutrons usually equal zero?

  • For an odd-A nucleus, how does the unpaired nucleon dictate the nuclear spin?

  • How can the magnetic moment of a nucleus be estimated using the shell model and the properties of the unpaired nucleon?

  • Explain the contribution of the g-factor to the calculation of a nucleus’s magnetic moment.

  • How does the Schmidt model approximate the magnetic moments of nuclei, and what are its limitations?

  • What physical properties of the nucleus influence its electric quadrupole moment?

  • How does a non-spherical charge distribution in a nucleus give rise to a measurable quadrupole moment?

  • Why do nuclei with spin I=0 or I=12 have no electric quadrupole moment?

  • For a nucleus with Z=21 and N=21, identify the valence nucleons and predict the ground-state spin and parity.

  • How does the spin-parity (Jπ) of the nuclear ground state depend on the orbital angular momentum of the valence nucleon?

  • Using the shell model, how would you predict the magnetic moment and quadrupole moment of 17O, assuming it has a single valence neutron in the 1d5/2 shell?