Question

A sample of carbon of mass 250 mg from wood found in a tomb underwent 2480 carbon- 14 disintegrations in 20 h. Estimate the time since death: assuming the modern sample underwent 1.84 times 10^4 disintegrations in the same time period.

Answer 1

Explanation:

Let the age to be found in years is y.

Hence,       $(2480 disintegrations) \times \frac{\frac{1.0g}{0.250g}}{1.84 \times 10^{4} disintegrations}$

                        = (\frac{1}{2})^{\frac{y}{5730yr}}

Solve for y as follows.

                    0.53913 = (\frac{1}{2})^{\frac{y}{5730yr}}

Now, taking log on both the sides as follows

               log 0.53913 = $(\frac{z}{5730}) log \frac{1}{2}$

               $\frac{log 0.53913}{log (1/2)}$ = $\frac{z}{5730}$

                       z = $\frac{5730 \times log 0.53913}{log (1/2)}$

                         = 5107 years

Thus, we can conclude that the time since death is 5107 years.