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 [l2, lz]. 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 l2 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)=Bexp (A,Z) - Btheor (A,Z), where Btheor (A,Z) is calculated using the semiempirical formula and Bexp (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.