Halflife Worksheet

1. 32P is used to treat some diseases of the bone.  Its half-life is 14 days.  Find the time it would take for a sample of 32P to decay from an activity of 10,000 counts per minute to 8,500 counts per minute.  

2. What would be the activity of the sample in question 2 above after 24 days?

3. A certain isotope has a half-life of 20 days.  How long would it take for a sample of this isotope to decay from 10,000 cpm (counts per minute) to 4000 cpm?

4. What would be the activity of the sample in question 1 after 10 days?

5. Vanadium-49 has a half-life of 330 days.  The initial activity of a 2g sample of this isotope is 20000 counts per minute (CPM).  How long will it take for the radiation of the isotope to go from 100 CPM to 50 CPM?

6. 48Cr has a half-life of about 24 hours.  If the initial activity of a sample of 48Cr is 3000, what would the activity be after 60 hours?

7. 131I transmutes to Xenon during the decay process.  How much Xe is produced after 400 grams of  131I is allowed to decay for 24 days?

8. How much time would have to elapse before the radioactivity in a piece of wood, due to 14C, would drop from 14 counts per minute to 8 counts per minute. (The half-life of 14C is 5730 years).

9. 59Fe has a half-life of 45 days.  If a piston ring had an initial activity of 10,000 counts per second what would the activity be after 100 days.

10. How much time would have to elapse in order for the activity of the piston ring in problem 9 to drop from 10,000 counts per second to 4000 counts per second.

11. At one time on the Historic Tour in the Mammoth Cave park in Kentucky an Indian, found in the caves was on display.  Because of the cave conditions the Indian's body was well preserved.  It was estimated that the indian was about 145 pounds and died at the age of 45 from a falling rock that crushed his spinal column.  Determine the approximate year of the Indian's death from the following data collected from the activity of 14C.

Assume the initial activity of 14C in his body was 15.7 cpm per gram of 14C

Current activity (circa 1950) ---11.76 cpm per gram of 14C.

Halflife of 14C --- 5730 years.

12 The data below was collected on the decay of an isotope.  Determine the halflife of the isotope by graphical analysis. You may plot either true activity vs. time or log(true activity) vs. time. All important calculations, similar to those requested in the lab, must be shown on the graph!

Day Activity
(cpm)
Background
(cpm)
Count time
(minutes)
true activity
(cpm)
log (true activity)
0 7466 40 4
2 6948 52 4
4 6472 60 4
6 5828 48 4
8 4796 52 4
10 4448 36 4
12 4072 36 4
14 3724 40 4
16 3284 40 4
18 3256 44 4
20 2728 56 4
22 2560 76 4
24 2384 72 4
26 2124 72 4
28 2004 72 4
30 1740 76 4


 
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