You are dating Moon rocks based on their proportions of uranium-238 (half-life o

Question

You are dating Moon rocks based on their proportions of uranium-238 (half-life of about 4.5 billion years) and its ultimate decay product, lead. Find the age for each of the following.

Part A

A rock for which you determine that 53 % of the original uranium-238 remains, while the other 47 % has decayed into lead.

Express your answer using two signficant figures.

Part B

A rock for which you determine that 63 % of the original uranium-238 remains, while the other 37 % has decayed into lead.

Express your answer using two signficant figures.

Explanation / Answer

We know that

A = A0 e^-kt

k = ln(2)/t1/2 = 0.693/4.5 = 0.154

It is stated that 53 % remains so

A = 0.53 A0

0.53 = e^-(0.154 t)

-0.154 t = ln 0.53

t = -0.635/-0.154 = 4.123 Years

Hence, t = 4.123 billion years

B)A = 0.63 A0

0.63 = e^-0.154 t

-0.154 t = ln 0.66

t = -0.462/0.154 = 3

Hence, t = 3 billion years

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