Transcript CH_9_4_HalfLife_of_a_Radioisotope

Chapter 9 Nuclear Radiation
1
9.4
Half-Life of a Radioisotope
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Half-Life and Decay Curves
2
The half-life of a radioisotope is the time for the radiation
level to decrease (decay) to one-half of the original value.
The decay curve for I-131 shows that one-half the sample
decays every 8 days.
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Half-Lives of Some Radioisotopes
3
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Guide to Using Half-Lives
4
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Half-Life Calculations
5
The radioisotope strontium-90 has a half-life of 38.1 years. If a
sample contains 36 mg of Sr-90, how many milligrams will
remain after 152.4 years?
Step 1 State the given and needed quantities.
Given: 36 mg, 152.4 years, half-life of 38.1 years
Needed: mg Sr-90 remaining
Step 2 Write a plan to calculate unknown quantity.
Half-life
152.4 years
number of half-lives
Number of half-lives
36 mg Sr-90
mg Sr-90 remaining
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Half-Life Calculations
6
The radioisotope strontium-90 has a half-life of 38.1 years. If a
sample contains 36 mg of Sr-90, how many milligrams will
remain after 152.4 years?
Step 3 Write the half-life equality and conversion factors.
1 half-life = 38.1 years
38.1 years
1 half-life
and
1 half-life
38.1 years
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Half-Life Calculations
7
The radioisotope strontium-90 has a half-life of 38.1 years. If a
sample contains 36 mg of Sr-90, how many milligrams will
remain after 152.4 years?
Step 4 Set up the problem to calculate amount of active
radioisotope.
Number of half-lives
4 years x 1 half-life = 4 half-lives
38.1 years
1 half-life
2 half-lives 3 half-lives 4 half-lives
36 mg  18 mg  9 mg  4.5 mg  2.3 mg Sr-90
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Learning Check
8
Carbon-14 was used to
determine the age of the Dead
Sea Scrolls. If the Dead Sea
Scrolls were determined to be
2000 years old and the half-life
of carbon-14 is 5730 years,
what fraction of this half-life
has passed?
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Solution
9
Carbon-14 was used to determine the age of the Dead Sea
Scrolls. If the Dead Sea Scrolls were determined to be
2000 years old and the half-life of carbon-14 is 5730 years,
what fraction of this half-life has passed?
2000 years x 1 half-life = 0.35 half-life
5730 years
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Learning Check
10
The half-life of I-123 is 13 h. How much of a 64-mg
sample of I-123 is left after 26 hours?
A. 32 mg
B. 16 mg
C. 8 mg
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Solution
11
The half-life of I-123 is 13 h. How much of a 64-mg sample
of I-123 is left after 26 hours?
Step 1 State the given and needed quantities.
Given: 64 mg, 26 hours, half-life of 13 hours
Needed: mg I-123 remaining
Step 2 Write a plan to calculate unknown quantity.
Half-life
26 hours
number of half-lives
Number of half-lives
64 mg I-123
mg I-123 remaining
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Solution
12
The half-life of I-123 is 13 h. How much of a 64-mg sample
of I-123 is left after 26 hours?
Step 3 Write the half-life equality and conversion factors.
1 half-life = 13 hours
13 hours
1 half-life
and
1 half-life
13 hours
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.
Solution
13
The half-life of I-123 is 13 h. How much of a 64-mg sample
of I-123 is left after 26 hours?
Step 4 Set up the problem to calculate amount of active
radioisotope.
Number of half-lives
26 hours x 1 half-life = 2 half-lives
13 hours
1 half-life
2 half-lives
64 mg  32 mg  16 mg I-123
The answer is B, 16 mg of I-123 remain.
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition
Copyright © 2012 by Pearson Education, Inc.