How old is the Menan Butte?

Carbon-14 Dating&

Potassium-Argon Dating

Carbon CycleThroughout its life span a living organism absorbs carbon from the atmosphere. When an organism dies the carbon-14 decays.

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

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!

Potassium-40 datingPotassium-Argon Dating

or K-AR dating

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!

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

Solving Exponential Equations

• If an equation has exponents we “root” both sides to solve for the variable.

• For example:

x2=4

X=2

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?

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

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

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.

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

Solve

Rate of decay!

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.

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!