Download Preview of Period 10: Nuclear Reactions

Preview of Period 10: Nuclear Reactions
10.1 Rates of Radioactive Decay
How can the half-life of a radioactive source
be used to find the age of the source?
How can capacitor discharge be used to model
radioactive decay?
10.2 Mass as a Form of Energy
How can the binding energy of a nucleus be
calculated?
10.3 Nuclear Binding Energy
How can the binding energy of a nucleus be
estimated from a binding energy graph?
10-1
Half -Life
♦ The half-life of a radioactive source is the
time required for half of the unstable nuclei
to decay.
♦ After one half-life, the material will be only
half as radioactive.
♦ The number of the original nuclei remaining
will be only half what it was originally.
Number of
Half Lives
0
Fraction of
Original
1
=
1
1
2
=
2
1
4
=
3
1
8
=
Number of
Half Lives
Fraction of
Original
1
6
20
1
1
64
7
1
128
=
8
1
256
=
9
1
512
=
21
1
22
1
2
4
1
16
=
5
1
32
=
3
1
24
1
10
=
1
=
1024
1
26
1
27
1
28
1
29
1
2 10
25
10-2
Exponential Growth and Decay
N = B x 2t
exponential growth:
exponential decay:
N =
B x 2
−t
=
B x
1
2t
N = the amount of the quantity at a given time
t = the number of time periods elapsed
B = the initial amount of the quantity
Example
A sample of radioactive material has a half life of
15 minutes. If there are 5.0 grams of the material
at the beginning of an experiment, how much will be
left after 1 hour has passed?
After 1 hour, four 15-minute half lives have passed.
N = B x
1
2t
= 5.0 grams
1
2
4
=
5.0 g
1
16
=
0.31 g
10-3
Carbon-14 Dating
14
Carbon-14 ( 6 C ) can be used to date
archeological sites
−
Carbon-14 decays be emitting a β particle
and an antineutrino
14
6C
→
14
7N
+
0
−1 e
+ ν
Carbon-14 is produced when cosmic rays
convert stable nitrogen-14 in the air into
carbon-14.
A
β + particle and a neutrino are emitted.
14
7N
→
14
6C
+
0
+1 e
+ ν
10-4
Carbon-14 Dating
♦ Both stable Carbon-12 and unstable Carbon14 isotopes are present in the atmosphere.
♦ Living organisms absorb both isotopes of
carbon.
♦ 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
1)
the ratio Carbon-12 to Carbon-14 in the
atmosphere at the time the organism died
2)
the present ratio of Carbon-12 to Carbon14 in the fossil, and
3)
the half-life of Carbon-14 (5,568 years)
10-5
Modeling Radioactive Decay with a Capacitor
Graph of Exponential Decay
1800
Charge Q (in microcoulombs)
1600
1400
1200
1000
800
600
400
200
0
0
3
6
9
12
15
Time (in seconds)
What is the Half-Life of the data represented by the
graph?
10-6
Finding the Half-Life of a Graph with
Background
1)
Pick a data point on your graph and read
the Y-axis value (the voltage in our case).
2)
Subtract the background voltage.
3)
Divide the result in half.
4)
5)
Add back in the background voltage. This
gives ½ the original voltage, corrected for the
background.
Find this voltage on your graph.
6)
Read down to the X-axis from this point to
find a time in seconds.
7)
The difference in seconds between this time
and the time of your original point is the
half-life – the time it took for ½ of the
capacitor’s charge to be released.
10-7
Nuclear Binding Energy Calculation: E = Mc2
Binding energy =
[(mass of unbound protons + neutrons)
– (mass of nucleus)] c2
Binding energy = [Z Mp + (A – Z) Mn – Mnuc] c2
Mp = mass of a free proton = 1.6726 x 10–27 kg
Mn = mass of a free neutron = 1.6749 x 10–27 kg
Mnuc = mass of the assembled nucleus in kg
Z
= number of protons in the nucleus
A-Z = number of neutrons in the nucleus
c2
= (speed of light)2 = (3 x 108 m/s)2
Binding energy per nucleon = binding energy
number of nucleons
converting units between MeV and joules:
or
1 Mev = 106 eV = 1.6 x 10–13 joules
1 joule = 6.25 x 1012 MeV
10-8
Nuclear Binding Energy Graph
10-9
Period 10 Summary
10.1 The half-life of an unstable element is the
time it takes on average for one half of the
nuclei in the sample to decay.
Radio-carbon dating uses the half life of
14
Carbon-14 ( 6 C ) to determine the age of
objects. Carbon-14 has a half life of 5,568
years.
10.2 Energy can be released when nuclei fuse
to form a nucleus that is more tightly
bound. In fusion reactions, light isotopes
release energy by combining (or fusing)
into heavier ones. Nuclear fusion is the
energy source that fuels stars.
10.3 Nuclear binding energy: the energy
required to hold nucleons together into
atoms.
The most stable nuclei have the greatest
binding energy per nucleon. Iron (Fe) has
high binding energy, while Uranium (U) has
less binding energy.
The energy released when nuclei fuse or
fission is calculated from E = Mc2
Binding energy = [(mass of unbound
protons + neutrons) – (mass of nucleus)] c2
Period 10 Review Questions
R.1 Carbon-14 dating cannot be used for
objects older than about 70,000 years.
Why should this be true? (Hint: the half-life
of C-14 is 5568 years.)
R.2 The half life of Ba-137 is about 2.6 minutes.
If you took a count rate from the Ba-137
30 minutes (about 12 half lives) after it
was extracted, could you estimate this
elapsed time well from such counting rate
data? Why or why not?
R.3 In class you used capacitor decay to model
radioactive decay and graphed the count
rate (voltage) per unit time. What was the
shape of your graph? Some graphs leveled
off at a count rate greater than zero. Why
was this the case?
R.4 The amount of matter converted into
energy in a chemical reaction is much
smaller than the matter converted into
energy in a nuclear reaction. Why is this?
R.5 You know the mass of a nucleus and the
number of protons and neutrons that make
up the nucleus. How would you find the
binding energy of the nucleus?