Question

A laboratory investigation shows that a sample of uranium ore contains 5.61 mg of ²³⁸₉₂U and 2.69 mg of ²⁰⁶₈₂Pb. Calculate the age (in y) of the ore. (The half-life of ²³⁸₉₂U is 4.47 ✕ 10⁹ y. The mass of a ²³⁸₉₂U atom is 238.050783 amu, and the mass of a ²⁰⁶₈₂Pb atom is 205.974449 amu.

______y (age)

Answer 1

First we determine millimoles of Pb-206:

2.69 mg / 206 mg/mmol = 0.013 mmol

Now Determine mg of U-238 that must have decayed:

0.013 mmol times 238 mg/mmol = 3.094 mg of U-238

Total U-238 present at start of decay:

5.61 mg + 3.091 mg = 8.704 mg

Determine how many half-lives have elapsed:

5.61 / 8.704= 0.645 (this is the decimal fraction of U-238 remaining)

(1/2)ⁿ = 0.645 (where n = the number of half-lives)

n log 0.5 = log 0.645

n* (-0.3010) = -(0.190)

n = 0.632

Determine how much time has elapsed:

4.5 x 10⁹ yr times 0.632 = 2.85 x 10⁹ yr