A sample of wood from an Egyptian mummy case gives a ¹⁴C count of 9.1 cpm/gC (counts per minute per gram of carbon). How old is the wood? (The initial decay rate of ¹⁴C is 15.3 cpm/gC, and its half-life is 5730 years.)

Question

Quizplus · Accepted Answer

The age of the wood can be calculated using the formula for radioactive decay: $ t = \frac{\ln(\frac{N_0}{N})}{\lambda} $, where $ N_0 $ is the initial count rate, $ N $ is the current count rate, and $ \lambda $ is the decay constant. The decay constant $ \lambda $ is related to the half-life $ T_{1/2} $ by $ \lambda = \frac{\ln(2)}{T_{1/2}} $. Substituting the given values, the age of the wood is approximately 4.3 x 10^3 years.

A Sample of Wood from an Egyptian Mummy Case Gives