Name:
Skill Sheet 29.1A
Radioactivity
In this skill sheet we are reviewing the concepts of radioactivity, radiation, and half-life. This will give you
practice in solving problems that include these terms.
1. Introduction to radiation
There are three main types of radiation that involve the decay of the nucleus of an atom:
•
alpha radiation (α):
4
release of a 2He nucleus
(two protons and two
neutrons).
•
beta radiation (β): release
of an electron.
•
gamma radiation (γ):
release of an
electromagnetic wave.
Radiation can also be released when two nuclei react (collide). In this case, radiation is one of the products of the
reaction. Also, in many cases, the collision creates an unstable nucleus — think of this type of nucleus as having
extra energy it must get rid of — which after a very short time releases energy in the form of radiation.
Conservation of energy and the use of Einstein’s formula (E = mc2) allow us to determine the amount of energy
released during a nuclear reaction or during a radioactive decay. The graphic below illustrates the decay of
carbon-14 to nitrogen-14.
Another example:
2
3
Consider the reaction of deuterium ( 1H , a proton and a neutron) and tritium ( 1H , a proton and two neutrons):
2
1H
3
4
+ 1H → 2He + n + energy
The energy released in this reaction is 2.8 × 10-12 joules. This energy is carried by the products of the reaction,
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( 2He and n). If we were to weigh the reactants and the products of this reaction, the difference in their mass
would be given according to Einstein’s formula by:
– 12
E- = ------------------------------------------2.8 × 10 joules- = 3.1 × 10 –29 kg
+ m n ) = ---2
8 2 2
2
2He
c
( 3 × 10 ) m /sec
Δm = ( m 2 + m 3 ) – ( m 4
1H
1H
1
Skill Sheet 29.1A Radioactivity
2. What is half-life?
The time it takes for half of the atoms in a sample to decay is called the half-life.
Example:
Four kilograms of a certain substance undergo radioactive decay. Let’s calculate the amount of substance left
over after 1, 2, and 3 half-lives.
•
After one half-life, the substance will be reduced by half, to 2 kilograms.
•
After two half-lives, the substance will be reduced by another half, to 1 kilogram.
•
After three half-lives, the substance will be reduced by another half, to 0.5 kilogram.
So, if we start with a sample of mass m that decays, after a few half-lives, the mass of the sample will be:
Number of half-lives
Mass left
1
1---m =
1
2
1--m
2
2
1---m =
2
2
1--m
4
3
1---m =
3
2
1--m
8
4
1
1
----- m = ------ m
4
16
2
3. Problems
1.
The decay series for uranium-238 and plutonium-240 are listed below. Above each arrow, write “a” for alpha
decay or “b” for beta decay to indicate which type of decay took place at each step.
→
234 Th
90
→
234 Pa
91
→
234 U
92
→
230 Th
90
→
226 Ra
88
→
222 Rn
86
→
218 Po
84
→
214 Pb
82
→
214 Bi
83
→
214 Po
84
→
210 Pb
82
→
210 Bi
83
→
210 Po
84
→
206
Pb
82
240Am
95
→
236 Np
93
→
232 Pa
91
→
232U
92
→
→
216 At
85
→
a. 238 U
92
Pu →
b. 240
94
2.
228 Bi
90
→
224 Ra
88
→
224 Ac
89
→
220 Fr
87
212 Bi
83
→
212 Po
84
→
208 Pb
82
→
208Bi
83
A large bomb releases about 5 × 1012 joules of energy. How much mass is converted into energy during such
an explosion?
2
Skill Sheet 29.1A Radioactivity
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3.
Fluorine-18 ( 9F ) has a half-life of 110 seconds. This material is used extensively in medicine. If the
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hospital laboratory starts the day (9 a.m.) with 10 grams of 9F , how many grams would be left after one
hour? Do you see a problem with this? How does the lab manage inventory?
4.
The isotope
5.
An isotope decreased to one-fourth its original amount in 18 months. What is the half-life of this radioactive
isotope?
14
6C
has a half-life of 5,730 years. What is the fraction of
14
6C
in a sample after 30,000 years?
4. The intensity of radiation
This diagram illustrates a formula that is used to calculate the intensity of radiation from a radioactive source.
Radiation “radiates” from a source into a spherical area. Therefore, you can calculate intensity using the area of a
2
sphere ( 4πr ). Use the formula and the diagram to help you answer the questions below.
1.
A radiation source with a power of 1,000 watts is located at a point in space. What is the intensity of
radiation at a distance of 10 meters from the source?
2.
The fusion reaction 1H + 1H → 2He + n + energy releases 2.8 × 10-12 joules of energy. How many such
reactions must occur every second in order to light a 100-watt light bulb? Note that one watt equals one joule
per second.
2
3
4
3