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General Physics (PHY 2140)
Lecture 37
¾ Modern Physics
9Nuclear Physics
9Radioactivity
9Nuclear reactions
http://www.physics.wayne.edu/~apetrov/PHY2140/
Chapter 29
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1
Lightning Review
Last lecture:
1. Nuclear physics
9 Properties of nuclei
9 Binding energy, types of radiation
A
Z
X
r = r0 A1/ 3
Review Problem: An alpha particle has twice the charge of a beta
particle. Why does the former deflect less than the latter when passing
between electrically charged plates, assuming that both have the same
speed?
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29.3 Radioactivity
Radioactivity is the spontaneous emission of radiation
Experiments suggested that radioactivity was the result
of the decay, or disintegration, of unstable nuclei
Three types of radiation can be emitted
„
Alpha particles
The particles are 4He nuclei
„
Beta particles
The particles are either electrons or positrons
„
„
„
A positron is the antiparticle of the electron
It is similar to the electron except its charge is +e
Gamma rays
The “rays” are high energy photons
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The Decay Constant
The number of particles that decay in a given time is proportional to
the total number of particles in a radioactive sample
∆N = −λ N ( ∆t )
„
λ is called the decay constant and determines the rate at which the
material will decay
The decay rate or activity, R, of a sample is defined as the number
of decays per second
∆N
R=
= λN
∆t
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Decay Curve
The decay curve follows the
equation
N = N 0 e − λt
The half-life is also a useful
parameter
The half-life is defined as the
time it takes for half of any
given number of radioactive
nuclei to decay
T1 2
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ln 2 0.693
=
=
λ
λ
5
Units
The unit of activity, R, is the Curie, Ci
„
1 Ci = 3.7 x 1010 decays/second
The SI unit of activity is the Becquerel, Bq
„
1 Bq = 1 decay / second
Therefore, 1 Ci = 3.7 x 1010 Bq
The most commonly used units of activity are the mCi
and the µCi
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QUICK QUIZ
What fraction of a radioactive sample has decayed after two halflives have elapsed?
(a) 1/4 (b) 1/2 (c) 3/4
(d) not enough information to say
(c). At the end of the first half-life interval, half of the original sample
has decayed and half remains. During the second half-life interval, half
of the remaining portion of the sample decays. The total fraction of the
sample that has decayed during the two half-lives is: 1 1 1
3
 
+  =
2 22 4
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29.4 The Decay Processes – General Rules
When one element changes into another element, the process
is called spontaneous decay or transmutation
The sum of the mass numbers, A, must be the same on both
sides of the equation
The sum of the atomic numbers, Z, must be the same on both
sides of the equation
Conservation of mass-energy and conservation of momentum
must hold
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Alpha Decay
When a nucleus emits an alpha particle it loses two
protons and two neutrons
„
„
„
N decreases by 2
Z decreases by 2
A decreases by 4
Symbolically
A
Z
„
„
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X→
A −4
Z −2
Y + He
4
2
X is called the parent nucleus
Y is called the daughter nucleus
9
Alpha Decay -- Example
Decay of 226Ra
226
88
Ra→
222
86
Rn+ He
4
2
Half life for this decay is 1600
years
Excess mass is converted into
kinetic energy
Momentum of the two particles
is equal and opposite
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QUICK QUIZ
If a nucleus such as 226Ra that is initially at rest
undergoes alpha decay, which of the following
statements is true? (a) The alpha particle has more
kinetic energy than the daughter nucleus. (b) The
daughter nucleus has more kinetic energy than the alpha
particle. (c) The daughter nucleus and the alpha particle
have the same kinetic energy.
(a). Conservation of momentum requires the momenta of the two
fragments be equal in magnitude and oppositely directed. Thus, from
KE = p2/2m, the lighter alpha particle has more kinetic energy that the
more massive daughter nucleus.
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Beta Decay
During beta decay, the daughter nucleus has the same
number of nucleons as the parent, but the atomic
number is one less
In addition, an electron (positron) was observed
The emission of the electron is from the nucleus
„
„
„
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The nucleus contains protons and neutrons
The process occurs when a neutron is transformed into a proton
and an electron
Energy must be conserved
12
Beta Decay – Electron Energy
The energy released in the decay
process should almost all go to
kinetic energy of the electron
Experiments showed that few
electrons had this amount of
kinetic energy
To account for this “missing”
energy, in 1930 Pauli proposed the
existence of another particle
Enrico Fermi later named this
particle the neutrino
Properties of the neutrino
„
„
„
„
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Zero electrical charge
Mass much smaller than the
electron, probably not zero
Spin of ½
Very weak interaction with matter
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Beta Decay
Symbolically
„
„
A
Z
X→ Z +A1Y + e − + ν
A
Z
X→ Y + e + ν
A
Z −1
+
ν is the symbol for the neutrino
ν is the symbol for the antineutrino
To summarize, in beta decay, the following pairs of
particles are emitted
„
„
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An electron and an antineutrino
A positron and a neutrino
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Gamma Decay
Gamma rays are given off when an excited nucleus “falls” to a lower
energy state
„
Similar to the process of electron “jumps” to lower energy states and giving off
photons
The excited nuclear states result from “jumps” made by a proton or neutron
The excited nuclear states may be the result of violent collision or more
likely of an alpha or beta emission
Example of a decay sequence
„
„
„
„
The first decay is a beta emission
The second step is a gamma emission
−
12
5
B→ C * + e + ν
12
6
C*→126 C + γ
12
6
The C* indicates the Carbon nucleus is in an excited state
Gamma emission doesn’t change either A or Z
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Uses of Radioactivity
Carbon Dating
„
„
Beta decay of 14C is used to date organic samples
The ratio of 14C to 12C is used
Smoke detectors
„
„
„
Ionization type smoke detectors use a radioactive source to ionize the
air in a chamber
A voltage and current are maintained
When smoke enters the chamber, the current is decreased and the
alarm sounds
Radon pollution
„
„
„
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Radon is an inert, gaseous element associated with the decay of radium
It is present in uranium mines and in certain types of rocks, bricks, etc
that may be used in home building
May also come from the ground itself
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29.5 Natural Radioactivity
Classification of nuclei
„
Unstable nuclei found in nature
Give rise to natural radioactivity
„
Nuclei produced in the laboratory through nuclear reactions
Exhibit artificial radioactivity
Three series of natural radioactivity exist
„
„
„
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Uranium
Actinium
Thorium
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Decay Series
of 232Th
Series starts with
232Th
Processes through
a series of alpha
and beta decays
Ends with a stable
isotope of lead,
208Pb
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29.6 Nuclear Reactions
Structure of nuclei can be changed by bombarding them
with energetic particles
„
The changes are called nuclear reactions
As with nuclear decays, the atomic numbers and mass
numbers must balance on both sides of the equation
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Problem
Which of the following are possible reactions?
(a) and (b). Reactions (a) and (b) both conserve total charge and total
mass number as required. Reaction (c) violates conservation of mass
number with the sum of the mass numbers being 240 before reaction
and being only 223 after reaction.
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Q Values
Energy must also be conserved in nuclear reactions
The energy required to balance a nuclear reaction is
called the Q value of the reaction
„
An exothermic reaction
There is a mass “loss” in the reaction
There is a release of energy
Q is positive
„
An endothermic reaction
There is a “gain” of mass in the reaction
Energy is needed, in the form of kinetic energy of the incoming
particles
Q is negative
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Problem: nuclear reactions
Determine the product of the reaction 3 Li + 2 He → ? + n
What is the Q value of the reaction?
7
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22
7
4
X
Determine the product of the reaction 3 Li + 2 He → Y ? + n
What is the Q value of the reaction?
Given:
reaction
In order to balance the reaction, the total amount of
nucleons (sum of A-numbers) must be the same on
both sides. Same for the Z-number.
Number of nucleons (A):
Number of protons (Z):
Thus, it is B, i.e.
7
3
Find:
Q=?
7 + 4 = X + 1 ⇒ X = 10
3+ 2 = Y + 0 ⇒ Y = 5
Li + 24 He → 105 B + 01n
The Q-value is then
(
)
Q = ( ∆m ) c 2 = m7 Li + m 4 He − m10 B − mn c 2 = −2.79MeV
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Threshold Energy
To conserve both momentum and energy, incoming particles must
have a minimum amount of kinetic energy, called the threshold
energy
KEmin
„
„
 m
= 1 +  Q
 M
m is the mass of the incoming particle
M is the mass of the target particle
If the energy is less than this amount, the reaction cannot occur
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QUICK QUIZ
If the Q value of an endothermic reaction is -2.17 MeV,
the minimum kinetic energy needed in the reactant
nuclei if the reaction is to occur must be (a) equal to
2.17 MeV, (b) greater than 2.17 MeV, (c) less than
2.17 MeV, or (d) precisely half of 2.17 MeV.
(b). In an endothermic reaction, the threshold energy exceeds the
magnitude of the Q value by a factor of (1+ m/M), where m is the
mass of the incident particle and M is the mass of the target nucleus.
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