Geologists who study volcanoes can develop historical profiles of previous erupt

Question

Geologists who study volcanoes can develop historical profiles of previous eruptions by determining the 14C-to-12C ratios of charred plant remains entrapped in old magma and ash flows. (t1/2 for 14C = 5730 y) Assume the samples were collected in AD 2008. What is the ratio of (14C/12C)2008 to (14C/12C)472 for the eruption of Mt. Vesuvius in AD 472? What is the ratio for the eruption of Mt. Vesuvius in AD 512? If the uncertainty in determining these ratios is 0.1%, could radiocarbon dating distinguish between debris from the eruptions of Mt. Vesuvius that occurred in AD 472 and AD 512? Number %

Explanation / Answer

Since the number of C12 atoms in the sample will remain will remain constant and only C14 will decay,

the ratio (14C/12C)2008 to (14C/12C)472 is actualy the ratio of (14C)2008 to (14C)472.

Now let N be the number of atom of 14C left in the sample in 2008 and N0 be that at 472 AD.

Then:        N = N0e-kt        {where k is the decay constant = 0.693/t1/2, and t = time elapsed }   

Given t1/2 for 14C = 5730 y, therefore k = 0.693/ 5730 y-1 = 1.2094 x 10-4 y-1, and t = 2008 -472 = 1536 y

therefore our required ration, N/N0 = e-(1.2094 x 10-4 x 1536) = 0.8305 or 83.05%

Now for the errupption in 512 AD, t = 2008 - 512 = 1496 y

therefore N/N0 = e-(1.2094 x 10-4 x 1496) = 0.8345 or 83.45 %

Yes radiocarbon dating can distinguish between the erruptions in 472 AD and 512 AD

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