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11/29/2010
1
Nuclear Binding, Radioactivity
• Sections 32-1 – 32-9
Physics 1161: Lecture 25
RadioactivitySpontaneous emission of radiation from the nucleus of an unstable isotope.
Marie Curie1867 - 1934
Wilhelm Roentgen1845 - 1923
Antoine Henri Becquerel1852 - 1908
Nucleus = Protons+ Neutrons
nucleons
A = nucleon number (atomic mass number)
Gives you mass density of element
Z =
N =
A=N+Z
Nuclear Physics
Li6
3
A
Z
Periodic_Table
A material is known to be an isotope of lead.
Which of the following can be specified?
1. The atomic mass
number
2. The neutron
number
3. The number of
protons
But protons repel one
another (Coulomb
Force) and when Z is
large it becomes
harder to put more
protons into a nucleus
without adding even
more neutrons to
provide more of the
Strong Force. For this
reason, in heavier
nuclei N>Z.
# neutrons vs # protons Where does the energy released in the nuclear
reactions of the sun come from?
1. covalent bonds
between atoms
2. binding energy of
electrons to the
nucleus
3. binding energy of
nucleons
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Strong Nuclear Force
• Acts on Protons and Neutrons
• Strong enough to overcome Coulomb
repulsion
• Acts over very short distances
Two atoms don’t feel force
Hydrogen atom: Binding energy =13.6eV
Binding energy of deuteron = or
2.2Mev!
2.2 × 10 6 eV
Simplest Nucleus: Deuteron=neutron+proton
neutron proton
Very strong force
Coulomb force
electron
proton
Strong Nuclear Force
(of electron to nucleus)
Binding Energy
Einstein’s famous equation E = m c2
Proton: mc2 = 938.3MeV
Neutron: mc2= 939.5MeV
Deuteron: mc2 =1875.6MeV
Adding these, gives
1877.8MeV
Difference is
Binding energy,
2.2MeV
MDeuteron = MProton + MNeutron – |Binding Energy|
Iron (Fe) has the most binding energy/nucleon. Lighter have
too few nucleons, heavier have too many.
BIN
DIN
G E
NE
RG
Y i
n M
eV
/nu
cle
on
92238U
10
Binding Energy Plot
Mass/Nucleon vs Atomic Number
Fusion
Fission
E = mc2
E: energy
m: mass
c: speed of light
c = 3 x 108 m/s
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E = mc2
• Mass can be converted to energy
• Energy can be converted to mass
• Mass and energy are the same
thing
Mass Defect in Fission
• When a heavy element (one
beyond Fe) fissions, the resulting
products have a combined mass
which is less than that of the
original nucleus.
Mass Defect of Alpha ParticleMass Defect of Alpha Particle
Mass difference = 0.0304 u
Binding energy = 28.3 MeV
Fusion product has less mass than the sum of the parts.
Which of the following is most correct for the
total binding energy of an Iron atom (Z=26)?
1 2 3 4
0% 0%0%0%
1. 9 MeV
2. 234 MeV
3. 270 MeV
4. 504 Mev
BIN
DIN
G E
NE
RG
Y i
n M
eV
/nu
cle
on
αααα particles: nucleii 24He
ββββ−−−− particles: electrons
γγγγ : photons (more energetic than x-rays)
3 Types of Radioactivity
Radioactive
sources
B field into
screen
detector
Alpha Decay
• Alpha decay occurs when there are too many protons in the nucleus which cause excessive electrostatic repulsion.
• An alpha particle is ejected from the nucleus.
• An alpha particle is 2 protons and 2 neutrons.
• An alpha particle is also a helium nucleus.
• Alpha particle symbol: 42He
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Beta Decay• Beta decay occurs when neutron to proton ratio is
too big• A neutron is turned into a proton and electron and
an antineutrino• The electron and the antineutrino are emitted
Gamma Decay
• Gamma decay occurs when the nucleus is at too high
an energy
• Nucleus falls down to a lower energy level
• High energy photon – gamma ray - is emitted
92238U→ 90
234 Th + αα: example 24He = αrecall
β: example
Decay Rules
1) Nucleon Number is conserved.
2) Atomic Number (charge) is conserved.
3) Energy and momentum are conserved.
γ: example γ00* +→ PP A
Z
A
Z
1) 238 = 234 + 4 Nucleon number conserved
2) 92 = 90 + 2 Charge conserved
−−+→ e01
1
1
1
0 pn
Needed to conserve
energy and momentum.
ν00+
A nucleus undergoes α decay. Which of the
following is FALSE?
1. Nucleon number decreases by 4
2. Neutron number decreases by 2
3. Charge on nucleus increases by 2
The nucleus undergoes decay. Which
of the following is true?β− 90
234 Th
1. The number of protons in the
daughter nucleus increases by one.
2. The number of neutrons in the
daughter nucleus increases by one.
Radioactive Decay
238
92U →
234
90Th→234
91Pa →
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U 238 Decay
• Decay Series
Nuclear Decay Links
• http://physics.bu.edu/cc104/uudecay.html
• http://www.physics.umd.edu/lecdem/honr22
8q/notes/U238scheme.gif
• http://www.physics.umd.edu/lecdem/honr22
8q/notes/fourdecschemes.gif
Which of the following decays is NOT allowed?
92238U→ 90
234 Th + α
HePbPo 4
2
210
82
214
84 +→
ν000
1
40
20
40
19 pK ++→ −− e
γ+→ NC 14
7
14
6
1.
2.
3.
4.
Decays per second, or “activity”:
If the number of radioactive
nuclei present is cut in half, how
does the activity change?
∆N∆t
= −λNNo. of nuclei
present
decay constant
1. It remains the same
2. It is cut in half
3. It doubles
Decays per second, or “activity”
Start with 16 14C atoms.
After 6000 years, there are only 8 left.
How many will be left after another 6000 years?
∆N∆t
= −λN No. of nuclei
present
decay constant
Every 6000 years ½ of atoms decay
1. 0
2. 4
3. 6
time
N(t ) =N0e−λt =N0 ⋅2
−t
T1/2
Decay Function
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Instead of base e we can use base 2:
N(t ) =N0e−λtSurvival:
No. of nuclei present
at time t
No. we started with
at t=0
e−λt = 2
−t
T1/2
T1/2 =
0.693
λwhere
Then we can write N(t ) =N0e−λt =N0 ⋅2
−t
T1/2
Half life
Radioactivity Quantitatively
∆N∆t
= −λN
No. of nuclei
present
decay constant
Decays per second, or
“activity”
Carbon Dating
• Cosmic rays cause transmutation of Nitrogen to Carbon-14
• C-14 is radioactive with a half-life of 5730 years
– It decays back to Nitrogen by beta decay
• The ratio of C-12 (stable) atoms to C-14 atoms in our
atmosphere is fairly constant – about 1012/1
• This ratio is the same in living things that obtain their carbon
from the atmosphere
1 14 1 14
0 7 1 6n N H C+ → +
14 0 14
6 1 7C e N−→ +
You are radioactive!
One in 8.3x1011 carbon atoms is 14C which β− decays with a ½
life of 5730 years. Determine # of decays/gram of Carbon.
∆N∆t
= −λN
( )
××
=
11
23
14103.8
11002.6
mole
12
0.1
gN
2/1
693.
T=λ
g
atoms 106
10×=
Carbon Dating
We just determined that living organisms
should have a decay rate of about 0.23
decays/ gram of carbon.
The bones of an ice man are found to have a
decay rate of 0.115 decays/gram. We can
estimate he died about 6000 years ago.
Summary• Nuclear Reactions
– Nucleon number conserved
– Charge conserved
– Energy/Momentum conserved
– αααα particles = nuclei
– ββββ---- particles = electrons
– γγγγ particles = high-energy photons
• Decays
– Half-Life is time for ½ of atoms to decay
N(t ) =N0e−λtSurvival:
T1/2 =
0.693
λ
24He
Mass/Nucleon vs Atomic Number
Fusion
Fission
Fusion
Fission
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U-235 -- Fissile Abundance of U-235
U-235 Fission
by
Neutron Bombardment
Possible U-235 Fission
Chain Reaction Breeder ReactionBreeder Reaction
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Breeder Reactor
• Small amounts of Pu-239 combined with U-
238
• Fission of Pu frees neutrons
• These neutrons bombard U-238 and
produce more Pu-239 in addition to energy
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