A sample of wood from an Egyptian mummy case gives a ¹⁴C count of 9.4 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: N(t) = N0 * (1/2)^(t/T), where N(t) is the current count rate, N0 is the initial count rate, t is the time elapsed, and T is the half-life. Solving for t gives t = T * (log(N(t)/N0) / log(1/2)). Substituting the given values: t = 5730 * (log(9.4/15.3) / log(1/2)) ≈ 4.0 × 10^3 years.

A Sample of Wood from an Egyptian Mummy Case Gives