PHYS 3330 Module 4 Self Assessment Practice Problems

Module 4 Self Assessment Practice Problems

4.1
The half-life of strontium-91, 91Sr is 9.70 h. Find
(a) its decay constant
(b) for an initial 1.00-g sample, the activity after 15 hours.
Answer: (a) 1.99 × 10−5 s−1 (b) 4.51 × 1016 decays/s
4.2
World War II aircraft had instruments with glowing radium-painted dials. The activity of one such instrument was 1.0 × 105 Bq when new.
(a) What mass of 226Ra was present?
(b) After some years, the phosphors on the dials deteriorated chemically, but the radium did not escape. What is the activity of this instrument 57.0 years after it was made?
Answer: (a) 2.73 µg (b) 9.76 × 104 Bq
4.3
If a radioactive nuclide decays for an interval of time equal to its average life, what fraction of the original activity remains?
Answer: 36.8%
4.4
How much time is required before a 3.7×108 Bq sample of 99mTc (T1/2 = 6.0 hours) and a 9.25×108 Bq sample of 113mIn (T1/2 = 1.7 hours) possess equal activities.
Answer: 3.14 h
4.5
How many becquerels of 24Na should be ordered so that the sample activity will be 3.7×108 Bq when it arrives 24 hours later?
Answer: 1.12 x 109 Bq
4.6
(a) What is the mass in grams of 3.7×109 Bq of pure 32P(T1/2 = 14.3 days)?
(b) How many 32P atoms constitute 3.7×109 Bq?
(c) What is the mass in grams of 3.7×109 Bq of Na3 32PO4 if all the phosphorus in the compound is radioactive?
Answer: (a) 3.5 x 10-7 g (b) 6.6 x 1015 atoms (c) 1.8 x 10-6 g
4.7
A source of cobalt 60 with half-life of 5.2 years has an activity of 1100 Ci.
(a) Express this activity in becquerels.
(b) Estimate the activity after 55 years.
Answer: (a) 4.07 x 1013 Bq (b) 2.04 x 1013 Bq
4.8
A source of gold-198 with a half-life of 2.69 days has an initial activity of 5 Ci. Calculate the activity after 4.0 days. Express this activity in becquerels.
Answer: 6.6 x 1010 Bq
4.9
The half-life of gold-198 is 2.69 days. Calculate the decay constant and the mean lifetime.
Answer: 0.258 d-1, 3.88 d
4.10
The physical half-life of 131I is 8.0 days.
(a) A sample of 131I has a mass of 100 µg. How many 131I atoms are present in the sample?
(b) How many 131I atoms remain after 20 days have elapsed?
(c) What is the activity of the sample after 20 days?
(d) What activity should be ordered at 8 am Monday to provide an activity of 8.2 × 104 MBq at 8 am on the following Friday?
Answer: (a) 4.6 × 1017 (b) 8.1 × 1016 (c) 8.2 × 104 MBq (d) 11.6 × 104 MBq