Students in a medical physics class are given the assignment of planning a nuclear medicine facility. They not only design the rooms and choose the major equipment, they also will have to solve elementary problems dealing with treatment, doses, radiation protection and safety, and the general principles of the physics of typical isotopes that might be used in diagnostic nuclear medicine. They are required to be familiar with concepts of half life, half-thickness for shielding and the decay schemes of representative isotopes.
(i) The most common isotope used in diagnostic work is Technetium. It is furnished from a generator or “cow” in which the negative beta decay of Molybdenum-99 produces the desirable metastable isotope of Technetium according to the following decay scheme?
42 Mo 99 → z Tc A + –1 e 0
(i) What are the atomic number, Z and mass number A, of the Tc isotope?
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Ans.
(i)
Sol. Both the total nucleon number and the total charge are constant in a nuclear reaction. The number of nucleons is the sum of all protons and all neutrons, whereas the charge number is the sum of all proton charges. Here the total charge is 42 and the total number of nucleons is 99. Thus: 42 = Z –1 or Z = 43 for Tc and
99 = A + 0 so that A = 99 for Tc and 99 = A + 0 so that A = 99 for Tc.
(ii)
Sol. Given that the half life (the time for one half the original nuclei to decay) is 67 hours for Mo 99 , we find that 5.5 days is very nearly two half-lives. Thus after 5.5 days only 1/4 or 0.25 remains.
(iii)
Sol. The effective half-life is given by the expression 1/Te = 1/T phy + 1/T bio , so that the effective values is always less than either T phy or T bio . One should be able to answer the question without knowing the exact form of the above equation by realizing that biological excretion helps rid the body of the original radioactive material at the same time it is decaying. (There is only one answer, A, smaller than T phy )
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