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molly16

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## Homework Statement

Geologists are able to calculate ages of rock samples through measurements of certain isotopic rations combined with known radioactive decay rates (all such decays being considered to adhere to 1st order kinetic rate laws). Two such processes leading to stable isotopes are:

87Rb --> 87Sr

238Ur --> 206Pb

Half life of 87Rb is 4.90x10^10 years while half life of 238Ur is 4.51x10^9 years.The isotopic ratios are:

87Sr/87Rb = 0.051

206Pb/238Ur = 0.71

Assuming the time the rock was formed it contained no 87Sr or 206Pb Calculate the age of the rock indicated by the isotopic ratios.

## Homework Equations

dA/dt = -k[A]

ln(A/Ao) = -kt

t1/2 = ln(2)/k

## The Attempt at a Solution

I tried solving for the rate constant using t1/2 = ln(2)/k

and rearranging it to k = ln(2)/t1/2 = 1.41 x 10^-11

Then to solve for the time for the decay of 87Rb I plugged the value into the equation ln(A/Ao) = -kt

ln (A/Ao) = ln (87Sr/87Rb) = ln (0.051) = -(1.41x10^-11)t

then I solved for t which is t = 2.1x10^11 years for the decay of the 87Rb

but the answer is supposed to be t = 3.517x10^9 years

Can someone please explain this question to me and tell me what I'm doing wrong?

Thanks!

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