(a)List the factors on which the rate of chemical reaction depends.
(b) The half-life for decay or radioactive `""^(14)C` is 5730 years. An archaeological artefact containin wood has only `80%` of the `""^(14)C` activity as found in living trees. Calculate the age of artefect.

Answer

1845 years

Explanation

`(N)/(N_(0))=80% or 0.80`
`t_(1//2)=5730 years`
`k=(0.693)/(t_(1//2))=(0.693)/(5730years)=1.21xx10^(-4)year^(-1)`
`k=(2.303)/(t)log``(N_(0))/(N)`
`1.21xx10^(-4)=(2.303)/(t)log``(1)/(0.8)`
`T=(2.303)/(1.21XX10^(4))log1.25`
`=(2.303)/(1.21xx10^(-4))log1.25`
`=(2.303)/(1.21xx10^(-4))xx0.0969=1845years`
Alternatively
Use direct relation,
`(t_(80%))/(t_(1//2))=(log(100)/(80))/(0.3)`
`t_(80%)=(5730years xx log0.8)/(0.3)~~1845years.`