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 Z

1

= N

2

and Z

2

= N

1

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
two mirror nuclei

15

8

O and

15

7

N.

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?

4. The radioactive isotope

198

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 t

1

= 10 h and t

2

= 12 h.

5. (a) Find the radius of the

12

6

C nucleus. (b) Find the force of repulsion between a proton at the surface

of a

12

6

C nucleus and the remaining five protons. (c) How much work (in MeV) has to be done to

overcome this electrostatic repulsion to put the last proton into the nucleus? (d) Repeat (a), (b),
and (c) for

238

92

U.

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 Wo loszyn
http://fatcat.ftj.agh.edu.pl/~woloszyn/phys/