Question

Suppose that an Egyptian farmer claims to have discovered a linen burial cloth used during Egypt's Middle Kingdom some 4000 years ago. Careful analysis shows that the cloth contains 80% of the ^{14}{\rm C} that it is estimated to have originally contained. How old is the cloth?

Answer 1

Answer:

the cloth is old by 1,844 years

Explanation:

The computation is shown below:

The half-life of C^(14) is 5730 years

Now

$\lambda$ =1.210 × 10^-4 years^(-1)

Now

$N(t) = Ce^{-\lambda\times t}$

$0.8 \times (N_0) = N_0 \times e^{-\lambda \times t}\\\\ln(0.8) = (-\lambda \times t)\\\\t = \frac{-(ln(0.8))}{\lambda}$

$\lambda$ = .000121,

so t = 1844 yrs

hence, the cloth is old by 1,844 years