1. General Physics (PHY 2140) Lecture 37 Modern Physics Nuclear Physics
Radioactivity
Nuclear reactions
Chapter 29
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2. Lightning Review Last lecture: Nuclear physics Properties of nuclei
Binding energy, types of radiation
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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3. 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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4. 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
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
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5. Decay Curve The decay curve follows the equation
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
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6. 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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7. QUICK QUIZ
What fraction of a radioactive sample has decayed after two half-lives 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:
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8. 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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9. 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
X is called the parent nucleus
Y is called the daughter nucleus
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10. Alpha Decay -- Example Decay of 226Ra
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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11. 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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12. 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
The nucleus contains protons and neutrons
The process occurs when a neutron is transformed into a proton and an electron
Energy must be conserved
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13. 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
Zero electrical charge
Mass much smaller than the electron, probably not zero
Spin of ½
Very weak interaction with matter
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14. Beta Decay Symbolically
 is the symbol for the neutrino
is the symbol for the antineutrino
To summarize, in beta decay, the following pairs of particles are emitted
An electron and an antineutrino
A positron and a neutrino
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15. 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
The C* indicates the Carbon nucleus is in an excited state
Gamma emission doesn’t change either A or Z
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16. Uses of Radioactivity Carbon Dating Smoke detectors Radon pollution
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
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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17. 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
Uranium
Actinium
Thorium
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18. 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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19. 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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20. Which of the following are possible reactions?
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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21. 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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22. Problem: nuclear reactions
Determine the product of the reaction
What is the Q value of the reaction?
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23. Determine the product of the reaction
What is the Q value of the 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.
Given:
reaction
Find:
Q = ?
Number of nucleons (A):
Number of protons (Z):
Thus, it is B, i.e.
The Q-value is then
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24. Threshold Energy
To conserve both momentum and energy, incoming particles must have a minimum amount of kinetic energy, called the threshold energy
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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25. QUICK QUIZ
If the Q value of an endothermic reaction is 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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