Title: Decay Rates
1Decay 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
2Decay 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
3Decay 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
4Decay 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
5Decay 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
6Decay 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
7Half-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,
8Decay 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
9Decay Series
- These start with the following nuclei
10Decay Series
11Radioactive 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
12Stability 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.
13Nuclear 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
14Nuclear 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
15Nuclear Reactions
- Rutherford observed the first nuclear reaction
with alpha particles - We often write this in shorthand as
16Nuclear 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
17Nuclear 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.
18Neutrons 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
19Neutrons and Uranium
20Neutrons 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
21Neutrons 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.
22Neutrons Uranium
23Neutrons Uranium
The extra neutrons released enable a chain
reaction to occur.
24Nuclear 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
25Nuclear 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
26Nuclear Fission
27Nuclear 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
28Nuclear Fusion
29Nuclear 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.