Radioactive dating uses the ratio of the amount of radioactive substance remaini

Question

Radioactive dating uses the ratio of the amount of radioactive substance remaining in a substance at time t, A(t) to the original amount in the substance (A_0)to estimate the age of the substance. The formula used is A(t) = A_0 e^kt. A (t) is the ratio, k is the decay constant, whose value depends on the substance, t is the time the substance has been decaying. The k-value for potassium-40 (K_40) is -0.000541= -5.41*10^-4 when time is measured millions of years. The symbol for potassium in the periodic chart is K. K_40 is potassium-40. Don't confuse it with the k-constant. Calculate the half-life of potassium-40. The half-life is the time that it takes for one-half of the original amount of a substance remain, as discussed in example 4.2.13. Solve for t, to two decimal places. Let A_0 be the original amount of the substance (at time t = 0). Then 0.5A_0 = A_0 ellipsis

Explanation / Answer

A(t)=A0ekt

0.5A0=A0e-.000541t

ln(0.5)=-.000541t

t=1281.23 years

ANd that's the answer .

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