Radioactive decay is a first`-` order process. Radioactive carbon in wood sample decays with a half`-` life of 5770 years. What is the rate constant `(` in years `)` for the decay ? What fraction would remains after 11540 years ?

Explanation

We have `lamda= (0.6932)/(t_((1)/(2)))`
`=(0.6932)/(5770)=1.2 xx 10^(-4)` per year
Further, as the duration of 11540 years is just the double of `t_((1)/(2))` (i.e., 5770 years) we can find out the fraction remained after 11540 years without using equation (24) as follows: After 5770 years, half of the substance would remain and after another 5770 years (i.e., a total of 11540 years) half of the half would remain, i.e., one fourth would remain after 11540 years.