Answer: 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.
