“Modeling Radioactive Half-Life” Answers
Radioactive Isotope
Half-life
239
94Pu
2.44 x 104 years
238
92U
4.51 x 109 years
214
84Po
0.00016 seconds
210
83Bi
5 days
210
82Pb
20.4 years
14
5.73 x 103 years
6C
Preliminary Questions:
1) Which of the radioactive isotopes in the table above would release the most radiation during a
30 day exposure? Explain.
214
84Po
This isotope would release the most radiation in 30 days because it emits radiation the
most often.
2) If carbon-14 decays into nitrogen, what is the decay particle that is emitted?
The decay particle emitted from carbon-14 is 
Data & Analysis:
1) Construct the graph with your cube data. Do the graphed sets of data indicate a constant or
non-constant rate of decay?
The best fit lines should be curved. Curves indicate non-constant change.
General Questions:
1) Based on the half-life's for each color on the cubes, which of these substances, red, black, or
white, do you think would be the most harmful? Why?
This is really an opinion question.
Ciardi, T Half‐Life Answers 1 

The substance that decays most rapidly will result in the highest dose of radiation in a
certain amount of time.
The substance the decays most slowly will result in radiation exposure lasting for the
longest amount of time.
2) The radioactive isotope
210
83Bi
decays by emitting a regular alpha particle.
a) What is the resulting isotope?
206
81Tl
b) If we start with 1000 grams of the
life of this isotope is 5 days.
Amount (grams)
1000
500
250
125
62.5
31.3
15.6
7.81
3.91
1.95
0.977
210
83Bi,
how much will be left after 50 days? The half-
Time (days)
0
5
10
15
20
25
30
35
40
45
50
c) Will the Bismuth-210 ever completely disappear? Explain.
Yes, eventually the last atom will decay, just as the last block rolled up white.
210
3) Two rocks are found at different levels in the Earth. Both contain the isotope 82Pb.
However, one rock contains 1/128th the amount of this isotope as the other rock. What is the
210
difference in the age of these rocks? The half-life of 82Pb is 20.4 years.
Amount (grams)
1
1/2
1/4
1/8
1/16
1/32
1/64
1/128th
Ciardi, T Time (days)
0
20.4
40.8
61.2
81.6
102
122.4
142.8
Half‐Life Answers One rock is 142.8 years older than
the other rock. 2