how old is the menan butte? carbon-14 dating & potassium-argon dating
TRANSCRIPT
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How old is the Menan Butte?
Carbon-14 Dating&
Potassium-Argon Dating
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Carbon CycleThroughout its life span a living organism absorbs carbon from the atmosphere. When an organism dies the carbon-14 decays.
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Carbon-14 dating• Radiocarbon dating (or carbon dating) is a
technique that uses the decay of carbon-14 to estimate the age of organic materials, such as wood and leather, up to about 58,000 to 62,000 years.
• Carbon dating has been used to date many well-known items, including samples of the Dead Sea Scrolls, the iceman, and many others
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No more Carbon?• After about 62,000 years there isn’t
organic material left to date using carbon dating.
• A fossil for example has had all of it’s organic material replaced with minerals.
• We can test something like Volcanic ash that surrounds the fossil and contains a naturally occurring radioactive element: POTASSIUM!
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Potassium-40 datingPotassium-Argon Dating
or K-AR dating
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Potassium-40 Dating• Potassium–argon dating or K–Ar dating is a method
used in archaeology. It is based on measurement of the radioactive decay of potassium (K) into argon (Ar).
• Potassium is a common element found in many materials. In these materials, the decay product 40Ar is able to escape the liquid (molten) rock, but starts to accumulate when the rock solidifies.
• Time is calculated by measuring the ratio of the amount of 40Ar accumulated to the amount of 40K remaining.
• The long half life of 40K allows the method to be used to calculate the age of samples older than a few thousand years!
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Solving Equations
• Before we jump head first into calculating equations for dating lets have a little refresher…
• When solving an algebraic equation we solve for the variable by adding, subtracting, multiplying, and dividing the same values to both sides of an equation to isolate a variable.
• For example: 2x+9=152x+9-9=15-9
2x=62x/2=6/2
X=3
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Solving Exponential Equations
• If an equation has exponents we “root” both sides to solve for the variable.
• For example:
x2=4
X=2
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Logarithms• But what if the exponent is a
variable?100 = 10x
Sometimes these can be easy to do in our heads. Such as the one above.
102 is 100.
But what about when the numbers don’t work out so nicely?
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Solving a Logarithmic Equation
Rewriting a logarithmic equation: solves for the exponent!
102=100Log 10100=2
A natural logarithm uses the natural number e (2.718…) for continuous growth and decay of natural materials. This is rewritten as ln (Natural Logarithm)
OR
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Half-Life• We will use the logarithmic formula:
• A = final amount • Ao = initial amount
• e = the natural number• r = rate of decay• t = number of years• We will have to use the Half life to find the rate of decay:
What % can we use for the final and the initial amount for half-life?
The half-life of carbon-14 is about 5,730 years.Potassium-40 is has a very long half-life of 1.248×109 years
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Potassium-40
The Menan Butte is a cinder cone volcano
When it erupted it laid down a layer of ash that we can measure the amount of radio-active potassium-40 and then give it a date.
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Solving the Logarithm Equation for Radioactive Dating
• Half life helps determine the rate of decay • Potassium has a half life of 1.248x109 years• We will use the Final Amount as 50% and Initial amount as 100%
to coordinate with the half-life
• A = 50% or .5• Ao=100% or 1
• T= 1.248x109 or 1,248,000,000
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Solve
Rate of decay!
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Cont.
• Now that we have the rate of decay we can find the age of the Butte.
• However, we don’t have the amount of potassium found in the ash on the Menan Butte….
• Let’s just suppose there is 99.99% of radioactive potassium.
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Solve• Final amount = 99.99% or .9999• Initial amount = 100% or 1• Rate of decay = -5.55 x 10-10 or -.000000000555
If the Menan Butte had 99.99% of potassium in the ash it would be 180,057 years old!