Calculating the age(chemistry)...?

Question

The cloud shroud from around a mummy is found to have a 14C(14 is upper-left corner of carbon) activity of 8.9 disintegrations per minute per gram of carbon. From the half-life of 14C decay, 5715 yr, calculate the age of the shroud.

Thank you for the help

10 points

Answer 1

Start by calculating the decay rate of fresh C14.  Divide the half life by ln 2 to get the natural period; this is 8245 years, which is 8245 x 24 x 60 x 365 = 1.2E7 minutes  Divide into 6E23 to get a disintegration rate of 4.7565E16 pops per mole per minute, or 3.964E15 pops per gram per minute.  Divide this by 8.9 to get the relative rate: 4.45E14.  The natural log of this is 33.73.  Multiply by the period to get 278,103 years.  There are probably simpler ways.