Physics tutorial #08
1. A radioactive sample has an initial activity of 2 mCi. After a decay time of 4.5 days, the activity
is found to be 1.41 mCi. Determine for this source (a) the decay constant, (b) half-life, and (c) the
number of nuclei in the sample initially.
2. A pair of nuclei of which Z1 = N2 and Z2 = N1 are called mirror isobars (the atomic and neutron
numbers are interchangeable). Binding energy measurements on these nuclei can be used to obtain
evidence of the charge independence of nuclear forces (that is, proton-proton, proton-neutron, and
neutron-neutron forces are approximately equal). Calculate the difference in binding energy for the
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two mirror nuclei O and N.
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Answer: 3.53 MeV
3. A freshly prepared sample of a certain radioactive isotope has an activity of 10 mCi. After an elapsed
time of 4 h, its activity is 8 mCi. (a) Find the decay constant and half life of the isotope. (b) How
many atoms of the isotope were contained in the freshly prepared sample? (c) What is the sample s
activity 30 h after it is prepared?
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4. The radioactive isotope Au has a half-time of 64.8 h. A sample containing this isotope has an
initial activity (t = 0) of 40 µCi. Calculate the number of nuclei that will decay in the time interval
between t1 = 10 h and t2 = 12 h.
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5. (a) Find the radius of the C nucleus. (b) Find the force of repulsion between a proton at the surface
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of a C nucleus and the remaining five protons. (c) How much work (in MeV) has to be done to
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overcome this electrostatic repulsion to put the last proton into the nucleus? (d) Repeat (a), (b),
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and (c) for U.
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6.  Free neutrons have a characteristic half-time of 12 min. What fraction of a group of free neutrons
at thermal energy (0.04 eV) will decay before travelling a distance of 10 km?
Answer: 0.0035
Nivas Babu Selvaraj, Maciej Woloszyn
http://fatcat.ftj.agh.edu.pl/~woloszyn/phys/