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12/22/12
Period 19 Solutions: Beta Decay and Its Applications
In beta plus decay, a proton changes into a neutron. In beta minus decay, a neutron
changes into a proton. In this period, we see how these changes take place.
10.1 What Is the Composition of a Nucleon?
Your instructor will discuss the composition of nucleons, which consist of quark trios
held together by gluon clouds.
1)
Quarks
a) What is a quark?
Quarks are the fundamental particles that make up neutrons and
protons.
i)
ii)
What is the electric charge of an “up” quark?  2
3
What is the electric charge of a “down” quark?  1
3
b) What is the spin of a quark?
Like almost all particles, quarks have a rotation about their axes called
intrinsic spin. The intrinsic spin of quarks (and leptons) = ½.
c) Place two of the green model “down” quarks side by side. In which directions do
the spins of two quarks point?
The spins of two quarks of the same type must point in opposite
directions. If the spin of one of the down quarks points in one direction,
the other down quark must be placed so that its spin points in the
opposite direction.
2)
Formation of Neutrons
Place orange or green “quarks” into the metal “gluon cloud” to represent a
neutron. (Hint: what is the electric charge of a neutron?)
a) The small circles in the diagram below represent quarks. On the diagram, write a
U for up or D for down in each circle to indicate the type of quark. Draw a vertical
arrow through each quark to represent the quark’s spin. There are two possible
arrangements of quarks for a neutron.
OR
u
b)
d
u
d
Each
½.
spin of a
1
d
d
quark has a spin of
What is the total
neutron? __1/2__
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c) Why does this arrangement of the 3 quarks result in a spin of ½ for the
neutron?
Since each quark has a spin of ½, the spins of two of the quarks will
point in the same direction (spin = ½ + ½ = 1), and the spin of the
third quark must point in the opposite direction. Two quarks of the
same type cannot have the same spin direction, therefore, the spins
of the two down quarks must point in opposite directions.
3)
Formation of Protons
Place orange or green “quarks” into the metal “gluon cloud” to represent a proton.
Make sure the spin of the proton points in the same direction as the spin of the
neutron in part a). (You may need to rotate the metal gluon cloud.)
a)
Write U for up or D for down on each quark. Draw arrows to represent each
quark’s spin.
d
u
u
OR
d
u
u
b)
What is the total spin of a proton? __1/2__
c)
Why does this arrangement
OR of the 3 quarks result in a spin of ½ for the proton?
Similar to the neutron, the spins of two of the quarks will point in the
same direction (spin = ½ + ½ = 1), and the spin of the third quark
must point in the opposite direction. Since two quarks of the same
type cannot have the same spin direction, the spins of the two up
quarks must point in opposite directions.
d) Which of the four fundamental forces is involved in binding quarks into nucleons?
the strong nuclear force
e) The exchange of which type of gauge boson is responsible for binding quarks into
nucleons? the gluon
f) Group Discussion Question: How is the gluon cloud model of a nucleon related to
flipping an orange or a white chip?
Flipping the chip represents the change of a nucleon from one type to
another. The gluon cloud model shows what happens inside the nucleon
during this change.
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19.2 Beta Decay in Carbon Nuclei
4) Carbon-14
a) What common radioactive isotope is used for archeological dating?
The carbon-14 isotope ( 146 C )
b) Why is this isotope unstable?
Carbon-14 is a small nucleus (only 6 protons) with an unequal number
of protons and neutrons.
c) What change to a
14
6C
nucleus would make it a more stable nucleus?
If one neutron decayed into a proton, the nucleus would have equal
numbers of neutrons and protons (7 of each type of nucleon).
d) Write a nuclear equation to show how a 146 C nucleus decays to become a more
stable nucleus. What type of ionizing radiation is emitted during this decay?
14
6C

14
7N

0
1 e
 
Since changing a neutron into a proton adds one positive charge, a
negatively charged electron (   particle) must be emitted to conserve
electric charge. An antineutrino is also emitted whenever an electron
is given off.
e) Where does carbon-14 come from? Write a nuclear reaction to show the
formation of 146 C .
The energy from cosmic rays can turn stable nitrogen-14 in the air into
carbon-14. One proton in the nitrogen atom turns into a neutron. An
antielectron (a positron) and a neutrino are emitted.
14
14
7N  6C

3
0
1 e
 
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19.3 A Model of Radioactive Decay
Your instructor will explain how to use a board that simulates radioactive decay with
circuit elements and a capacitor.
5) Finding the half-life of a radioactive source
a) What is the half-life of a radioactive source?
The half-life of a radioactive source is the time required for half of the
unstable nuclei to decay. After one half-life, the number of the original
nuclei remaining will be only half what it was originally, and the
material will be only half as radioactive. After 2 half-lives, only one
fourth of the original radioactive material will remain.
b)
After charging the capacitor, flip the switch to the right to allow the capacitor to
discharge through the resistor. At the same time, start the timer. Measure the
voltage with a multimeter set to measure DC voltage ( V ) every 15 seconds
for four minutes. Record your measurements in the table below.
Time
elapsed
(Min: Sec)
Voltage
(volts)
Time
elapsed
(Min: Sec)
0:00
2:15
0:15
2:30
0:30
2:45
0:45
3:00
1:00
3:15
1:15
3:30
1:30
3:45
1:45
4:00
Voltage
(volts)
2:00
a) Make a graph on the grid below of the voltages you measured versus time
elapsed.
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18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
15
30
45
60
75
90
105
120 135 150
Time (in seconds)
5
165 180
195 210
225 240
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b) What is the smallest voltage reading you obtained? __ approximately 3
volts__
c) What does this voltage represent? Why didn’t your graph decrease further?
This voltage represents the background radiation.
d) Would your graph decrease below this voltage if you had measured the voltage
for a longer time? Why or why not?
No, the background radiation (in this case, background voltage) is
always present.
e) From your graph, find the half-life represented by the capacitor’s discharge. To
do so, you must subtract the background radiation (the background voltage),
find the time for the radiation (the voltage) to decrease by ½, and then add in
the background radiation (background voltage).
Pick a data point on your graph as your starting point for the voltage.
Subtract the background voltage. Divide the result in half. Then add back
in the background voltage. This gives ½ the original voltage, corrected
for the background. Find this voltage on your graph. The time elapsed
between this point and your original point is the half-life – the time it took
for ½ of the capacitor’s charge to be released.
6) Carbon Dating
a) How long does it take for one-half of the carbon-14 nuclei in a sample to decay?
5,730 years
b) How can the half-life of carbon-14 allow us to determine the age of an
archeological object?
Both stable carbon-12 and unstable carbon-14 isotopes are present in
the atmosphere (in carbon dioxide). Living organisms absorb both
isotopes of carbon in the process of respiration. After an organism
dies, it no longer absorbs any new carbon-14, and the carbon-14 within
it decays. We can accurately estimate the time of an organism's death,
if we know the ratio carbon-12 to carbon-14 in the atmosphere at the
time the organism died, the present ratio of Carbon-12 to carbon-14 in
the fossil, and the half-life of carbon-14.
c) A sample of bone from an archeological site was found to contain only one-sixty
fourth (1/64) the amount of carbon-14 that would have been present in living
bone at the time this organism was alive. What is the age of this bone?
Since
1
1
 6 we know that 6 half-lives have passed since this
64
2
organism died.
6 half lives x 5,730 years
half life
6
= 34,380 years
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d) Group Discussion Question: An archeological team works in a dig they believe to
be around one million years old. Would carbon-14 dating be appropriate to
determine the age of this site? Why or why not?
No, after one million years, so many half-lives would have passed that
the amount of Carbon-14 left would be very small.
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