A sample of wood from an Egyptian mummy case gives a count of 8.5 cpm/gC (counts per minute per gram of carbon).How old is the wood? (The initial decay rate of
Is 15.3 cpm/g C,and its half-life is 5730 years.)

Question

A sample of wood from an Egyptian mummy case gives a  count of 8.5 cpm/gC (counts per minute per gram of carbon).How old is the wood? (The initial decay rate of 
Is 15.3 cpm/g C,and its half-life is 5730 years.)

Quizplus · Accepted Answer

We can use the equation for exponential decay:

A=A₀(e^(-rt))

where A₀ is the initial count rate, A is the count rate after time t, r is the decay rate, and e is Euler's constant (approximately 2.718).

We know the initial count rate (A₀) is 15.3 cpm/gC and the count rate (A) is 8.5 cpm/gC, so we can solve for the time (t):

8.5 = 15.3(e^(-0.693t/5730))

0.5556 = e^(-0.693t/5730)

ln(0.5556) = -0.693t/5730

t = (-5730/0.693) ln(0.5556)

t ≈ 2005 years

Therefore, the wood is approximately 2005 years old, which corresponds to answer choice C.

A Sample of Wood from an Egyptian Mummy Case Gives