Question

Could someone please help me with this? Assume that the half-life of ^14C is 6000 years. State the estimated age of a sample of mummified skin from a prehistoric human that contained 6.25 percent of an original quantity of ^14C.

Answer 1

Given:

half life of $^{14}C , t_{\frac{1}{2}}$ = 6000 years

%quantity contained in sample,  $N_{t}$ = 6.25% $N_{o}$ original quantity = 0.0625$N_{o}$

Formula used:

Formula for carbon dating is given by:

$t = \frac{\ln \frac{N}{N_{o}}}{-0.693}.t_{\frac{1}{2}}$

where,

$N_{t}$ = amount of radio active material

$N_{o}$ = amount of original material

$t_{\frac{1}{2}}$ = half life

Solution:

Using the formula mentioned above with suitable values given:

$t = \frac{\ln \frac{0.0625N_{o}}{N_{o}}}{-0.693}\times 6000$

$t = \frac{\ln 0.0625}{-0.693}\times 6000$

t = 24005.097 years

Therefore, the estimated age of the sample of the mummified skin is 24005.097 years