Question

A meteor contains 0.556 g of pb-206 to every 1.00 g of u-238. assuming that the meteor did not contain any pb-206 at the time of its formation, determine the age of the meteor. u-238 decays to pb-206 with t1/2 = 4.5 x 109 y

Answer 1

Answer is: 2,94·10⁹ years.
m(Pb) = 0,556 g.
n(Pb) = m÷M = 0,556g÷206g/mol = 0,0027mol.
m(Au) = 1,00g.
n(Au) = 1g÷238g/mol =0,0042mol.
n(Pb)/n(Au) = 0,575
t1/2 = 4,5·10⁹ years.
λ = 0,693÷t1/2, λ = 0,693÷4,5·10⁹ = 0,154·10⁻⁹.
λ-decay constant
Use this formula: λ·t = ln(1+ n(Pb)/n(Au)
ln - natural log.
t = 0,453÷0,154·10⁻⁹ = 2,94·10⁹ years.