Marian Physics
Half Life
Flat Prairie Publishing
Half Life
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The half life of a radioactive
sample is the amount of
time it takes half of the
radioactive nuclei to decay.
Section 1
Half Life
Half Life
The half life of a radioactive sample is the time it takes half of
the nuclei in the radioactive sample to decay.
For example, consider a radioactive isotope that has a half life
of 10 minutes. If you start with a sample of 1,000 nuclei, after
10 minutes 500 of them on average will have decayed. We cannot predict which nuclei will decay but we can say with some
certainty that about 500 will decay. In the next 10 minutes 250
of the remaining 500 nuclei will decay. Every 10 minutes ½ of
the remaining nuclei will decay.
One of the cool things about this decay is that no matter how
many nuclei you start with in one half life ½ of the nuclei will decay. An interesting example of an exponential function.
Equations:
Where N is the number of particles remaining after time t.
N0 is the number of nuclei at time t=0
is the decay constant and is proportional to the half life.
t is the time.
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You can also use M and M0 instead of N and N0 if the mass
units are consistent.
where t1/2 is the half life.
A equals the activity in decays/second. One decay/second is
called a Becquerel (Bq)
A0 is the activity at time t=0.
is the decay constant.
t is the time.
Now for some problems:
1. An isotope of cesium (cesium-137) has a half life of 30 years.
If you start with 1 kg of cesium-137, how much cesium will be
left after 90 years.
2. You put 100 grams of pure Carbon-14 in a jar and set it aside
for 11,460 years. At the end of that time you find that you
have 25 grams of Carbon-14 left in the jar. What is the half
life of Carbon-14?
3. Nitrogen-16 has a half life of 7.13 seconds. Someone puts
and unknown quantity of Nitrogen in a container and starts a
timer. When the timer hits 54 seconds you open the container and discover that there are 54 grams of Nitrogen-16 in
the container. What was the original mass of Nitrogen-16 in
the container?
And now for something completely different.
Her hair glistened in the rain like nose hair after a sneeze.
A is the activity at time t and N is the number of remaining nuclei at time t.
4. Thallium-208 has a half-life of 3.053 min. How long will it take
for 120.0 g to decay to 7.50 g?
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5. A radioactive isotope has an activity of 10,000 Bq. What will
the activity be after 2 half lives?
6. A radioactive isotope has an activity of 344 Bq. Two days
later the activity has fallen to 43 Bq. What is the half life and
decay constant for this isotope?
She had a deep, throaty, genuine laugh, like that sound a dog
makes just before it throws up.
7. A radioactive isotope has an original activity of 15,000 Bq
and a half life of 100 seconds. What is the decay constant for
this isotope?
8. How many atoms were originally present in the sample?
12. Carbon-14 has a half-life of 5730 years and is used to date
archaeological objects. All living organisms have a constant
carbon-12/carbon-14 ratio. When the organism dies carbon12 levels remain constant but carbon-14 decays. The changing carbon-12/carbon-14 ratio can be used to determine the
date of the artifact. For example, fresh charcoal made from
a tree contains carbon-14 which will give a radioactive
count of 13.60 disintegrations per minute per gram of carbon. Prehistoric cave paintings were found in Spain. A piece
of charcoal found in the ancient cave in Altamira, Spain
gave 1.70 disintegrations per minute per gram of carbon.
From this information, determine the age of the cave paintings.
She grew on him like she was a colony of E. coli and he was roomtemperature Canadian beef.
9. What will be the activity of the sample after 20 minutes?
10. How many atoms have decayed after 5 minutes (not remaining but decayed)?
11. 10 mg of iodine-131 is given to a patient. The half life of
iodine-131 is 8 days, How much iodine-131 is left in the patient 24 days later.
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17. How many atoms will remain after 10 minutes?
18. How many atoms decayed during the first 5 minutes?
19. What is the activity after 200 seconds?
20. You prepare a pure sample of a radioactive substance. After 30 minutes, 45% of the original sample is left. What is
the half life of the radioactive substance?
21. A radioactive sample has an activity of 16,000 Bq and an
half life of 16 minutes. What will the activity be after 16 minutes? (yes this should be a gift).
The graph above shows the decay of a radioactive sample. The
initial activity is 5000Bq.
13. What is the half life of the isotope?
Long separated by cruel fate, the star-crossed lovers raced across
the grassy field toward each other like two freight trains, one having
left Cleveland at 6:36 p.m. traveling at 55 mph, the other from
Topeka at 4:19 p.m. at a speed of 35 mph.
14. What is the decay constant?
15. What will be the activity of the sample after 9 minutes?
16. How many atoms of the isotope were originally in the sample?
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