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.