22.01 “Introduction to Ionizing Radiation”
Fall 2006
Problem Set #3
Due Date: Tuesday, October 3, 2006
Show all work. Provide units on all answers.
1. The activity of a radioisotope is found to decrease to 45% of its original value in 30
days.
(a) What is the decay constant?
(b) What is the half-life?
(c) What is the mean life?
2. How long will it take for each of the following radioisotopes to decrease to 0.0001%
of its initial activity?
64
(a)
Copper
41
(b)
Scandium
99
(c)
Technetium
99m
(d)
Technetium
3. A sample contains 1.0 GBq of 90Sr and 0.62 GBq of 90Y.
(a) What will be the total activity of the sample 10 days later?
(b) What will be the total activity of the sample 29.12 years later?
4. The global inventory of 14C is about 8.5 x 1018 Bq. If this entire inventory is a result
of cosmic ray interactions in the atmosphere, how many kilograms of 14C are produced
each year in the atmosphere?
5. Calculate the number of grams contained in a 5 mCi source of the following nuclides:
(a) 18F
(b) 14C
(c) 32P
(d) 235U
6. Charcoal found in a deep layer of sediment in a cave is found to have an atomic
14 12
C/ C ratio only 30% that of a sample from a higher level with a known age of 1850
years. What is the age of the deeper layer?
7. Technicium 99m (99mTc) is used for nuclear medicine imaging procedures. The
minimum dose that generates a useful image is 5 mCi. Generally, each patient receives
10-15 mCi for an imaging procedure. 99mTc is produced by elution from “generators”
containing the bound parent isotope 99Mo. A radioisotope generator is calibrated to
contain 500 mCi of 99Mo at 12 noon on Friday, Sept 22. The generator containing 99Mo
is delivered on Monday morning at 6 am.
(a) The 99mTc is eluted at 8 am on Monday, Sept 25. How much 99mTc is eluted (in mCi)?
(b) The generator is then eluted on Wed, Sept 27 at 8 am. Is there enough 99mTc available
for 10 patient imaging studies?
(c) What is the last date that the generator can be used to produce enough 99mTc for a
patient study (i.e., > 5 mCi)?
8. A uranium ore sample contains the daughter 226
88 Ra , which has a half-life of 1620
years. Chemical analysis shows that the ratio of the number of atoms of 226Ra (N226) to
the number of atoms of 238U (N238) is N226/N238 = 4.34 x 10-7. Show how this
information can be used to calculate the half-life of 238U.
9. Elemental analyses on 5 separate samples from the same meteorite gave the following
data, expressed in atoms/sample. How old is this meteorite?
Sample
1
2
3
4
5
87
Rb
1377
16500
4050
24390
16848
87
Sr
3913
12540
1661
7157
4001
86
Sr
5511
16500
2025
8130
4212