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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.

Respuesta :

Explanation:

Let the age to be found in years is y.

Hence,       [tex](2480 disintegrations) \times \frac{\frac{1.0g}{0.250g}}{1.84 \times 10^{4} disintegrations}[/tex]

                        = (\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 = [tex](\frac{z}{5730}) log \frac{1}{2} [/tex]

               [tex]\frac{log 0.53913}{log (1/2)}[/tex] = [tex]\frac{z}{5730}[/tex]

                       z = [tex]\frac{5730 \times log 0.53913}{log (1/2)}[/tex]

                         = 5107 years

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

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