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
or have no electric quadrupole moment?For a nucleus with
and , identify the valence nucleons and predict the ground-state spin and parity.How does the spin-parity (
) 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
, assuming it has a single valence neutron in the shell?