General Physics PHY 2140

1
General Physics (PHY 2140)
Lecture 37

• Modern Physics
• Nuclear Physics
• Radioactivity
• Nuclear reactions

http//www.physics.wayne.edu/apetrov/PHY2140/
Chapter 29
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?
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

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
• ? 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

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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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

7
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
QUICK QUIZ
(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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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

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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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

11
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.
QUICK QUIZ
(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
• The nucleus contains protons and neutrons
• The process occurs when a neutron is transformed
  into a proton and an electron
• Energy must be conserved

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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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

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 doesnt 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
• 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
• 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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Which of the following are possible reactions?
Problem
(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 What is
the Q value of the reaction?
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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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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

25
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.
QUICK QUIZ
(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.