Question

In a museum a wooden article is placed which has 40% activity of C ^ 14 as compared to a green wood; predict the age of this wood if half-life of C ^ 14 is 5770 years.​

Answer 1

Given:

In a museum a wooden article is placed which has 40% activity of C ^ 14 as compared to a green wood.

To find:

Age of the wood ?

Calculation:

Let the number of half lives after which this magnitude of activity has been achieved be "n"

$\therefore \: 40\% = \bigg({ \dfrac{1}{2} \bigg) }^{n}$

$\implies\: \dfrac{40}{100} = \bigg({ \dfrac{1}{2} \bigg) }^{n}$

$\implies\: \dfrac{4}{10} = \bigg({ \dfrac{1}{2} \bigg) }^{n}$

$\implies\: \dfrac{2}{5} = \bigg({ \dfrac{1}{2} \bigg) }^{n}$

$\implies\: log_{10} \bigg(\dfrac{2}{5} \bigg) = n \times log_{10} \bigg( \dfrac{1}{2} \bigg)$

$\implies\: ( - 0.39)= n \times ( - 0.3)$

$\implies\: n = 1.3$

So, age of wood:

$\therefore \: T = t_{ \frac{1}{2} } \times n$

$\implies \: T = 5770 \times 1.3$

$\implies \: T = 7501 \: yrs$

So, age of wood is 7501 years.