What is the half-life associated with each of the following decay constants?

Applied Nuclear Physics      Decay Law             Homework 8

 

1. What is the half-life associated with each of the following decay constants?

(a) 0.523/day;  (b) 0.035/second;  (c) 1.25/minute.

 

 

 

 

 

 

 

 

2. What is the decay constant associated with each of the following half-lives?

(a) 8.20 days;  (b) 3.4 x 10^-3 second;  (c) 2.2 minutes.

 

 

 

 

 

 

 

 

 

 

3. Barium-137m has a half-life of 2.50 minutes. If a sample of Barium-137m has an initial activity of 2.00 microcuries, what is the activity at t =

(a) 1.00 minute?  (b) 2.00 minutes?  (c) 8.00 minutes?  (d) 15.0 minutes?

 

 

 

 

 

 

 

 

 

 

4. The decay constant of a radioactive source is 0.150/second. The initial mass of the source is 4.2 micrograms.  What is the mass of the source at t = (a) 0.200 second?  (b) 4.80 seconds?  (c) 10.0 seconds?  (d) 12.0 seconds.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5. The decay constant of a radioactive source is 0.300/minute. How much time must elapse before the activity is reduced to (a) 85%?  (b) 25%?  (c) 5%?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6. The half-life of a radioactive source is 14.0 minutes. How much time must elapse before the activity is reduced by (a) 70%?  (b) 45%?  (c) 20%?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7. Radon-222 has a physical half-life of 30.0 days. A 10.24 microgram piece of this source is placed in storage.  (a) How much mass is in the form of Radon-222 after 56 days?  (b) How much time must elapse before the mass of Radon-222 is reduced to 5%?

 

 

 

 

 

 

 

 

 

 

 

 

 

8. A radioactive source has an initial activity of 3.00 millicuries. After 10.0 hours, the activity of the source is 1.50 millicuries.  (a) What is the half-life of the source?  (b) What is the decay constant of the source?

 

 

9. A radioactive source has a decay constant of 0.139/second. How many radioactive atoms are present when the source has an activity of (a) 3.00 microcuries?  (b) 50.0 millicuries?  (c) 1.00 curie.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10. A radioactive source has a half-life of 14.0 minutes. Its activity is 5.00 microcuries at 10:00 AM. (a) What is the decay constant of the source?  (b) How many parents are present at 10:00 AM?  (c) What is the activity at 10:48 AM?  (d) How many parents are present at 10:48AM? (e) How many disintegrations occur between 10:00 AM and 10:48 AM?  (f) How many daughters are born during this time interval?

 

 

 

 

 

 

 

 

 

 

 

 

 

11. Find the initial activity at 10:00 a.m. of a source with a decay constant of 0.150/hour if the final activity is (a) 25.3 mCi at noon. (b) 8.31 µCi at 1:30 p.m. (c) 40.2 mCi at 3:00 p.m.   (d) 58.2 µCi at 6:30 p.m.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

12. What must be the minimum total activity of Tc-99m at 10:00 a.m. if you are to derive 25.0 mCi 11:00 a.m., 30.0 mCi at 12:30 p.m. and 15.0 mCi at 2:00 p.m. from the total? The decay constant of Tc-99m is 0.115/hour.