Decay Rates

1
Decay Rates

• If we have a radioactive nucleus, we want to
  consider the rate at which a sample of the
  material will decay
• Each nucleus has an apparent lifetime, that is it
  can decay at any time, but on average, so many
  will decay in any given time period
• We need to examine the implications

2
Decay Rates

• What the apparent lifetime translates into is a
  probability that any given nucleus will decay in
  a given time period
• Each nucleus in a sample has the same probability
  of decaying in the time period as any other
  nucleus
• So what can we say about what this means

3
Decay Rates

• If we have ten times as many nuclei in a sample,
  we would expect ten times as many decays in a
  given time period
• The number that decay is proportional to the
  number we have at present

4
Decay Rate

• The constant is called the decay constant
• The larger the decay constant, the faster the
  nuclei decay and the higher the probability of
  decay in a given time interval
• This means the lifetime of the nucleus is shorter

5
Decay Rate

• The equation describing the process looks just
  like the discharge rate of a capacitor through a
  resistor
• The number of decays per second is called the
  activity of the sample ?N/ ?t

6
Decay Rate

• By tradition, physicists like to talk about these
  decays in terms of a half-life
• This is the time it takes for half of a sample to
  decay
• We can do a little math to relate the half-life
  to the decay constant

7
Half-Life
After one-half life, half the sample will be
gone. After another half-life, half of that half
will be gone. If we started with 2000 nuclei, the
progression through several half-lives would be
2000, 1000, 500, 250, The rate declines in the
same way, 1000, 500, 250, 125,
8
Decay Series

• Many heavy nuclei that decay wind up having the
  daughter nucleus being unstable as well
• This process often continues for several
  generations
• There are three major naturally occurring decay
  series

9
Decay Series

• These start with the following nuclei

10
Decay Series
11
Radioactive Dating

• We can take advantage of radioactive decay to
  estimate the ages of various things
• We can date organic matter using C-14 created by
  cosmic ray neutrons striking N2 in the atmosphere
• We can date rocks using U-238 and comparing
  parent daughter ratios

12
Stability and Tunneling

• We mentioned before that alpha decay occurs by
  tunneling

The alpha particle tunnels through barrier and
emerges with the same energy it had inside the
nucleus. It has negative kinetic energy inside
the barrier. Use uncertainty principle!!! Same
thing happens with H in NH3.
13
Nuclear Reactions

• We can transform one element into another via a
  nuclear reaction
• We just talked about changing nitrogen into C-14
  via n N-14 - C-14 p
• This is called a transmutation
• Enormous number of possible reactions

14
Nuclear Reactions

• We need to balance equations just like we do for
  chemical reactions
• We can nucleons, which are conserved
• We count charges, which are conserved
• We have to conserve energy and momentum and
  angular momentum

15
Nuclear Reactions

• Rutherford observed the first nuclear reaction
  with alpha particles
• We often write this in shorthand as

16
Nuclear Reactions

• Reactions can be exothermic or endothermic
• Use Emc2
• Sum the energies of the reactants and the
  energies of the products
• The difference will be positive or negative

17
Nuclear Reactions
If Q0, the reaction is exothermic. If Qreaction is endothermic. For endothermic
reactions, there is a threshold KE necessary to
make the reaction go. You have seen this in
chemistry.
18
Neutrons Uranium

• Bombard U-238 nuclei with neutrons
• Two different sets of processes occur
• The first is simple neutron capture and
  subsequent decay of the resulting U-239 into a
  new element, neptunium-239
• The neptunium subsequently decays into another
  new element, plutonium-239

19
Neutrons and Uranium
20
Neutrons Uranium

• The second process that occurs is much more
  remarkable!!
• The uranium essentially broke approximately in
  half and yielded a variety of nuclei of barium,
  krypton, xenon, tin, molybdenum, strontium and
  additional neutrons!!!
• A model for the nucleus, the liquid drop model
  was developed to explain the results

21
Neutrons Uranium
The added from the entering neutron excites the
nucleus into an oscillatory stretching mode.
Once the nucleus stretches a bit, the proton
repulsion vastly outweighs the strong nuclear
force and the nucleus reaches a point of no
return and splits into chunks. MORE NEUTRONS
EMERGE!!! About 200 MeV of energy is released.
22
Neutrons Uranium
23
Neutrons Uranium
The extra neutrons released enable a chain
reaction to occur.
24
Nuclear Fission

• U-235 fissions and U-238 captures neutrons and
  produces plutonium which also fissions
• Make a nuclear reactor to produce a controlled
  fission process
• Absorb two of the neutrons that come out so only
  one goes on to produce another fission
• Use cadmium as the absorber

25
Nuclear Fission

• If you dont mop up the neutrons, the reaction
  can run away
• Then you have an fission bomb
• Can do with either U-235 or Pu-239
• Simply have to create a critical mass so that the
  neutrons can multiply

26
Nuclear Fission
27
Nuclear Fusion

• Go to the other end of the scale
• Put small nuclei together to form bigger ones and
  also get energy output
• Lets look once again at the binding energy graph

28
Nuclear Fusion
29
Nuclear Fusion

• Powers the sun and stars with various cycles
  leading to iron

Counting positron-electron annihilation the net
energy output is 26.7 MeV. Not as much as
fission, but per kg of fuel a much bigger yield.