22.101 Applied Nuclear Physics
(Fall 2004)
Due: Nov. 1, 2004
Problem Set No. 6
Problem 1
Use the semiempirical mass formula to calculate the mass of C12 and Bi209. Tabulate the
individual percentage contribution to the average binding energy per nucleon from the
volume, surface, Coulomb, asymmetry, and pairing terms. Compare your mass and B/A
results with experimental values from the Nuclide Chart.
Problem 2
Use the semi-empirical mass formula to determine which isobars with A = 140 should be
stable. Indicate the various modes of decay and the predicted stable isotope. Compare
your results with experimental data.
Problem 3
(a) You are given the series disintegration A → B → C → D (stable), with decay
constants λ A , λ B , λC respectively. Find the number of atoms of B, C, and D
collected in a time t if the activity of A is held constant. (This is the
approximation for a very long-lived source).
(b) Tellurium is bombarded by deuterons in a cyclotron, the reaction being
Te130 (d , p)Te131 → I 131 → Xe131 (stable)
with both decays being β − , and the half lives are 30 hours and 8 days
respectively. The bombardment conditions are such that the (d,p) reaction is
equivalent to a source strength of 2 mCi. Find
(i)
the initial rate of I131 production, in µCi per hour,
(ii)
the number of Xe131 atoms produced during a single 6-hour
bombaqrdment,
(iii)
the total number of Xe131 atoms obtained eventually if the target were
allowed to stand undisturbed for several months following a 6-hour
bombardment.