The ratio of carbon-14 to nitrogen in an artifact is 1: 1 . given that the half-life of carbon-14 is 5730 years, how old is the artifact?

5,728.5 years

Explanation:

By measuring the current ratio of daughter to parent, that is (Dt/Pt) one can deduce the age of any sample. The assumption is that there is no daughter atom present at time,t=0 and that the daughter atoms are due to the parent decay(where none has been lost).

Lamda= ln 2÷ half life,t(1/2)

Lamda= ln2= 0.693/5730 years

Lamda=1.21 × 10^-4

Using the formula below;

Age,t= 1/lamda× (ln {1+ Dt/Pt})(1)

Slotting our values into equation (1) above.

Age,t= 1/lamda(ln[1+1/1])

Age,t= 1/1.2×10^-4(ln 1+1)

Age,t= 1/1.21×10^-4(ln 2)

Age,t= ln 2/ 1.21×10^-4

Age, t= 5,728.5 years.

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