1. A given radioactive sample emits only one type of radiation. When placed in a counter for 10 minutes, 1632 counts are registered.
Then the sample is removed and a background of 2641 counts is registered in 90 minutes.
a) What is the net count per minute?
b) If the efficiency of the counter is 26% what is the activity of the source in Bq?
b) What is the standard deviation of the activity (in Bq)?
2. Calculate the commutator [l^{2}, l^{z}]. Use the properties [AB,C]=A[B,C] + [A,C]B and
[A,BC]=B[A,C] + [A,B]C along with the definition of l^{2} and lz.
3. Compare the proton separation energy for a nucleus with magic Z with that of its neighbours with Z+1 and Z-1. Discuss your findings.
4. Determine ΔB (A,Z)=B^{exp} (A,Z) - B^{theor }(A,Z), where B^{theor} (A,Z) is calculated using the semiempirical formula and B^{exp} (A,Z) using atomic masses. Do this for three nuclei with both proton and neutron magic numbers. Choose three nuclei: a light, a medium heavy and a heavy nucleus.
Discuss your findings.