S.O.S. Mathematics CyberBoard

Over geological time, an atom of 238U decays to a stable 206Pb atom. A geochemist analyzes a rock and finds that is contains 9.0 x10-5 cm3 of helium (at standard temperature and pressure) per gram and 2.0 x 10-7 g of 238U per gram. Estimate the age of the rock in years given that the half-life of 238U is 4.47 x109 .
HINT: see decay series of 238U

Hey kaven!!!!!this is bien, bellow here is the solution of question #12 that our teacher give out.



Solution or Explanation:
1. Helium = 9.0 x 10-8 L / 22.414 L/mol = 4.0153 x 10-9

2. delta decay in moles = 4.0153 x 10-9 / 8 = 5.0192 x 10-10 mol

3. remiaing U-238 = N = 2.0 x 10-7 g / 238 g/mol = 8.40336 x 10-10 mol U-238

4. initial U-238 = No = 8.40336 x 10-10 mol + 5.0192 x 10-10 mol = 13.422 x 10-10 mole U-238 (initial)

5. k = ln(2) / 4.47 x 109 yr = 1.5507 x 10-10 yr-1

6. ln (N/No) = -kt
thus t = ln (N/No) / -k = 3.02 x 109 yr