Geologists can estimate the age of rocks by their uranium-238 content. The urani

Question

Geologists can estimate the age of rocks by their uranium-238 content. The uranium is incorporated in the rock as it hardens and then decays with first-order kinetics and a half-life of 4.5 billion years. A rock is found to contain 83.0% of the amount of uranium-238 that it contained when it was formed. (The amount that the rock contained when it was formed can be deduced from the presence of the decay products of U238 .) Part A How old is the rock? Express your answer using two significant figures. t =

Explanation / Answer

half-life decay in first order
ln (Ao/At) = kt,


t = ( ln (Ao/At) ) / k

t(half) = ( ln 2 ) / k

t(half)= 4.5*10^9 yr.

k = ( ln 2 ) / t(half) = (ln 2)/(4.5*10^9 yr)

Then solve

k= 1.54*10^-10 yr^-1.

At = 83.2% of Ao,

At=0.830*Ao. That should give us all we need.

t = ( ln (Ao/At) ) / k

Put values
t = (ln (Ao/(0.832Ao)) / (1.54 * 10^-10 yr^-1)

Solve..
t=1.2 * 10^9 yr. ANSWER

I hope help you.....

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