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

Step-by-step explanation:

Let the age to be found in years is y.

Hence,
`(2480 disintegrations) * ((1.0g)/(0.250g))/(1.84 * 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 =
`((z)/(5730)) log (1)/(2)`

`(log 0.53913)/(log (1/2))` =
`(z)/(5730)`

z =
`(5730 * log 0.53913)/(log (1/2))`

= 5107 years

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