The Muon HalfLife Project

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The Muon Half-Life Project
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Intro

• In this course, you will learn about radioactive
  decay, what a half-life is, and how to use
  analysis tools associated with these concepts,
  including graphs and formulas related to decay.
  Then, you will use these tools to determine the
  half-life of a particle known as the muon

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Radioactive decay

• First, what is radioactive decay?
• Radioactive decay is the process by which an
  unstable subatomic particle emits other subatomic
  particles and energy.
• Radioactive materials have an important property
  called a half-life, which is useful in various
  applications, such as dating.

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Half-Life

• The term half-life refers to the time it takes
  for half of the amount of a radioactive substance
  to decay.

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Radioactive Substances

• Some well known radioactive substances are
• Uranium-238, Radium-226, Carbon-14
• Uranium-238 has a half-life of about 4.5109
  years
• The half-life of radium-226 is about 1600 years

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Radioactive Particles

• There are also radioactive particles such as free
  neutrons, pions, or muons.
• A free neutron has a half life of about 11
  minutes and decays into a proton, an electron,
  and an electron antineutrino
• Other neutrons do not decay because they are
  contained within stable nuclei.

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Carbon-14

• The half-life of carbon-14 is about 5730 years.
• Because all living things contain some carbon-14,
  it is very useful for dating objects made of
  organic compounds, such as ancient campfires, or
  ancient human remains.

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Carbon-14 (cont.)

• You may be thinking, Well, if carbon-14 is
  radioactive and decays, why haven't we run out?
• The reason we haven't run out is that carbon-14
  is continuously being produced in the atmosphere,
  and here's the cool thing, cosmic rays are
  responsible for this production.

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Carbon-14 (cont.)

• The production of carbon-14 is a two step process
• First, a cosmic ray collides with an atomic
  nucleus in the air, this produces neutrons and
  other junk
• The neutrons can then collide with Nitrogen-14 to
  produce carbon-14 and other junk
• The junk is quite interesting, but it is not
  involved with the story of carbon-14

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Carbon-14 (cont.)

• Carbon-14 dating works by measuring the amount of
  carbon-14 left in a sample and comparing it with
  the amount of carbon-14 the sample would contain
  when it was new.
• Example If you found an object that only had
  one quarter of its original carbon-14, it would
  be two half-lives, or 11460 years old.

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Carbon-14 (cont.)

• While organisms are alive (trees, humans,
  animals), they are taking in carbon-14 at the
  same rate as it is decaying. When the organisms
  die, the carbon-14 is no longer being replaced.
  Therefore, carbon dating is actually measuring
  the amount of time since an organism has died.

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Carbon-14 (cont.)

• Carbon-14 exhibits radioactive beta decay
• C-14 --gt N-14 electron electron antineutrino
• Because the atomic mass number stays the same,
  this means a neutron in carbon-14 is becoming a
  proton in nitrogen-14

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Beaninium Archeology

• In this activity, you will be dating samples of
  radioactive beaninium
• When a sample of beaninium is new, the red/white
  ratio is 1/1
• Beaninium has a half-life of 100 years
• One final note, when the white decay, they
  disappear. They do not turn into red. (i.e. the
  number of red is the count of the original amount
  of white)

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Samples
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Table

• Now, make a table that looks like this to keep
  your data about the samples

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Answers
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Twizzler Decay

• In this next activity, you will be responsible
  for the decay of a twizzler
• First, you will create a graph of the twizzler
  length vs half lives
• Mark the original length, then eat half. A
  half-life has now passed. Mark the length again
  and continue until the twizzler is gone.

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Twizzler Decay (cont.)

• The graph should look something like this

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Twizzler Decay (cont.)

• You will then find a formula for the length of
  twizzler after n half-lives

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Twizzler Decay (cont.)

• The equation should look something like this
• Where Ln is the current length and L0 is the
  original length

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Estimate of Age

• If you estimated the ages of G and H as 150 and
  75 years, we need to revise that estimate.
• These ages would be correct if the decay were
  completely linear, but we just found that the
  decay is a curve

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Estimate of Age (cont.)

• By comparing the curve and the linear fit, how
  should the age estimate for G and H be changed?
  Higher? or Lower?

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Decay Equation

• Now find an equation for the length of the
  twizzler at any time, not just for integer
  half-lives
• Hint How would you make an amount of time given
  the number of half-lives and the length of one
  half-life

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Decay Equation (cont.)

• Answer to Hint tnt1/2
• We then use this to find
• And the final equation should look like this

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Logs

• Properties of Logarithms
• log(ab)log(a)log(b)
• log(a/b)log(a)-log(b)
• log(an)nlog(a)

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Log Equation

• Now use the tools you have acquired to find the
  ages of samples G and H from the bean archeology
  activity
• Note This is the equation of a line ymxb

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Answers

• The age of sample G should be around 141 years
• The age of sample H should be around 68 years

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Whats a Muon?

• A muon is a heavy electron about 207 x mass of
  electron
• Discovered at Caltech in 1936 by Carl Anderson
  while studying cosmic rays
• The muon is radioactive and decays into an
  electron and two neutral particles called
  neutrinos
• This however, does not mean a muon is made of
  these things. It is a fundamental particle.

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The Muon Half-Life

• Because Muons are radioactive, they have a half
  life too, and were almost ready to discover what
  it is.
• But first, we are going to do a simulation.

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Coin Toss Activity

• This activity will simulate the muon half-life
  data you will be collecting later.
• Each coin represents a radioactive particle
• When the coin comes up tails, it has decayed.
• Keep track of how many tosses it took until the
  coin decayed (e.g. HHT would be 3 tosses until
  the coin decayed)

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Coin Toss (cont.)

• When making your table of surviving data, the
  pennies that survived after 1 toss are all of
  the pennies that had 2 or more tosses. Those
  that survived after 2 tosses are those that you
  tossed 3 or more times etc...
• Graph the number surviving vs tosses

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Linearize Graph

• Use the log equation we found before
• Graph log(number surviving) vs tosses
• It should be a straight line, or close
• Make a best fit line and find the slope
• The half-life of a penny should be one toss

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Muon Half-Life

• Now we are ready to find the half-life of a muon

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Cosmic Ray Detectors

• A cosmic ray detector consists of two parts, the
  scintillator, and the photomultiplier tube (PMT)
• Scintillator is a special plastic that emits
  light when a cosmic ray goes through it
• A PMT detects that light and sends a signal to
  the computer, indicating a cosmic ray has gone
  through

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Equipment

• The setup for this experiment consists of a shmoo
  (a chicos cosmic ray detector) on top of two
  other detectors, called paddles

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How it works

• The paddles are used to get a count of the
  particles that go into the shmoo, but do not go
  through the paddles
• Most muons pass right through the shmoo and the
  paddles, but if they stop inside the shmoo, they
  will decay into electrons
• When this decay happens, it produces two
  sequential flashes of light, and the computer can
  measure the time between them

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Get the data

• The data is available online at lt gt
• Go and download a unique set of data
• Copy your data into the spreadsheet

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Use the excel sheet

• This time the sheet is doing all the work you did
  for the coin toss experiment.
• It finds the number surviving and plots it vs
  time
• The sheet then linearizes the graph and
  calculates the half-life from the slope of the
  line
• Now you have found the half-life of a muon.