Radioactive Decay

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Radioactive DecayGlottochronology
An Archeological Adventure in Ancient Egypt

• Brought to you by
• Emily brown
• Meaghan daniels

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What a Discovery!

• Archeologist, Dr. Great and his team have just
  discovered the greatest find of the century.
• In the middle of the Sahara desert, a new
  civilization has been discovered.
• Before this discovery can be reported
• The team must identify its
• Ancestral heritage.
• How can they do that?

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Glottochronology

• Dr. Great and his team use glottochronology to
  determine when his civilization broke away from
  mainstream Ancient Egyptian culture
• He is uses a list of common words used during the
  Middle Kingdom.
• He counts how many words from the list are used
  by the civilization he discovered.
• Next he finds out how many words from the list
  are used by the mainstream Egyptian culture that
  existed during the same time his civilization
  existed.

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Glottochronology contd

• The reason we use lists from the Middle Kingdom
  (a period before the two languages diverged) and
  one from the New Kingdom was because both
  languages evolved after the split.

Dr. Great's Civilization
1100 BCE
Middle Kingdom-Egypt 2000-1570 BCE
1700 BCE
New Kingdom- Egypt 1570-1085 BCE
Dates are approximate
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Glottochronology ContdHow to Do the Math.

• The language of Dr. Greats civilization includes
  85.8 of the words on the list of words from the
  Middle Kingdom.

• The language of the New Kingdom includes 89.9 of
  the words on the list of words from the Middle
  Kingdom.

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Multiplication Principle

• 85.8 89.9.771
• 0.771 a(n)/a(0), when a(n) words still in use
• a(0) words originally on the list

• To get an estimate of the number of words the two
  newer languages have in common, multiply the
  percentages together.
• This is the based on the multiplication principle.

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• The probability of any given word remaining in
  one language after 1,000 years is 80.5.
  Therefore, the probability of any given word
  remaining in two languages after 1,000 years is
  80.580.5. We use this to find the rate.

• Dynamical Function
• a(n1) r a(n)
• General Solution
• a(k) rk a(0)
• 0.8052 a(0)r1000a(0)
• 0.8052 r(1000)
• r 0.805.002
• a(n)(0.805.002)na(0)

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• a(n)(0.805.002)n a(0)
• a(n)/a(0) (0.805.002)n
• a(n)/a(0) 0.771
• 0.771(0.805.002)n
• log 0.771 n log (0.805.002)
• n log .771/ log(0.805.002)
• n600 years
• n 3100 3700 years ago

• We plug all our information into the equation to
  solve for n, which is the years since the
  civilizations diverged.
• We now add the known age of (3100) to n to find
  out how many years from today the civilizations
  diverged.

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Oh No!

• Dr. Great thought it was time for his crew to
  have a break,so they went on a holiday to the
  beach. Unfortunately, they left the site
  unguarded, and while they were gone a group of
  renegades and grave robbers discovered their site
  and took most of its archaeological treasures.

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A Few Weeks Later...
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At the World Renowned Institute for Old Stuff in
Ithaca, New York a Number of Peculiar Characters
Have Come Forward With Some Very Interesting
Artifacts they Claimed came From Dr. Greats
Civilization.

• Could these be the real deal or are they hoaxes?

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Carbon Dating

• The scientists decide to prove whether these
  artifacts are real or are forgeries using a
  technique called carbon dating.
• Carbon dating can be used to determine the age of
  some once living material, such as paper, cloth
  even human body tissue.
• In this case carbon dating can help rule out the
  artifacts that dont belong in the era of Dr.
  Greats civilization.

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How does the carbon get into the samples?

• In space Nitrogen atoms are blasted with
  neutrons, which produces Carbon-14 atoms and
  Hydrogen.
• 147N10n -- 146C11H
• The Carbon-14 combines with Oxygen to form CO2,
  which is used by plants in the respiratory
  process.
• The plants are then eaten by humans or used to
  make linen cloth. After the plants die, the
  intake of carbon-14 ends and the decay process
  begins.
• Carbon dating will tell us when these plants or
  people died and can then give us an idea of when
  the artifacts were used.

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How Carbon-dating Works

• The element carbon has 3 naturally occurring
  isotopes, carbon-12 (the most common form),
  carbon-13 and carbon-14.
• Carbon-14 is an unstable isotope. It
  radioactively decays by emitting b-particles.
• 146C -- 0-1e 147N

• The carbon-14 to carbon-12 ratio in lab
  samples of biological material is analyzed, and
  then compared to the ratio of carbon-14 to
  carbon-12 in modern samples.

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Carbon dating contd

• The greater the difference between the ratios,
  the older the sample is.
• Carbon-14 has a half-life of 5730 (,-) 40)
  years.
• Carbon dating only works for materials that are
  less than 10,000 years old.

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How to Do the Math

• Find the mass of carbon-14 in the sample. This
  can be done using a mass spectrometer.
• For this problem we are assuming that the amount
  of Carbon-14 in the atmosphere has remained
  constant since the beginning of time.

• Mass of the Carbon-14 in the artifacts sample is
  0.0285 g.
• Mass of the Carbon-14 in the modern sample is
  0.2356 g.

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• We are solving for n (the age of the artifact)
• In order to do this we need to find the rate of
  decay ( r).
• We can find this using half-life of Carbon 14.
• What is the half-life?

• Dynamical system
• a(n1) r a(n)
• General solution
• a(n) rn a(0)
• a(0) mass of C-14 in the modern sample
• a(n) mass of C-14 in the artifact

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• Carbon-14 has a half-life of 5730 years this is
  the k value.
• Use the general equation to solve for r for the
  rate of decay of carbon-14

• a(k) rk a(0)
• 0.5 a(0) r5,730 a(0)
• 0.5 r5,730
• r 0.5 1/ 5 730

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• Time to put it all together!!!!!

• A(n) rn a(0)
• 0.0285 (0.51/5730)n 0.2356
• 0.1210(0.5 1/5730)n
• log 0.1210n log (0.5 1/5730)
• n log 0.1210/ log (0.5 1/5730)
• n 17,459.8576 years old

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Data From the Artifactsand the Results
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Dr. Greats Civilization Enters the History Books
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Hey, What Do You Know?

• What you thought Dr. Greats adventures would end
  there? Of course not.
• On his next expedition Dr. Great discovers an
  unknown site outside of Mesopotamia, and he needs
  your help to identify the age of the
  civilization, and whether or not the artifacts
  are authentic. Hes sending the data over right
  now.

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The Language Data

• Known language
• 75.6 of the words are the same as a common
  ancestral language.

• Unknown language
• 78.3 of the words are the same as a common
  ancestral language.

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Carbon-14 Data From the Artifacts
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The Tough Questions

• When did Dr. Greats civilization break off from
  the mainstream civilization if we know that it
  existed around 4,700 BCE?
• What artifacts are authentic to this
  civilization? (remember that .2356 g of C-14 are
  found in modern samples)
• How old are the forgeries?

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Credits
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