Carbon-containing compounds in living organisms maintain an equilibrium with ""^(14)C in the atmosphere. The activity associated with C in the equilibrium is 15 disintegrations/minute/gram of carbon(t_(1//2) " of " ""^(14)C=5730 years). An old tree, found in an burial, was subjected to radioactive dating. The decay rate associated with its ""^(14)C content is 10 disintegrations/minute/gram of C. Find the time elapsed since the tree was cut down.

Carbon-containing compounds in living organisms maintain an equilibriu

1.	Carbon-containing compounds in living organisms maintain an equilibrium with ""^(14)C in the atmosphere. The activity associated with C in the equilibrium is 15 disintegrations/minute/gram of carbon(t_(1//2) " of " ""^(14)C=5730 years). An old tree, found in an burial, was subjected to radioactive dating. The decay rate associated with its ""^(14)C content is 10 disintegrations/minute/gram of C. Find the time elapsed since the tree was cut down.
Answer» SOLUTION :`lamda= (0.6932)/(5730)=1.21 xx 10^(-4) YR^(-1)` Now, rate of disintegration of `""^(14)C` (when equilibrium was destroyed, i.e., when the tree was cut down) `prop N^(0)`. And present rate of disintegration `prop N` i.e. `(N^(0))/(N)= (15)/(10)` Using EQN (24), `lamda= (2.303)/(t) "log" (N^(0))/(N)` or `1.21xx 10^(-4) = (2.303)/(t) "log" (15)/(10)` or `t=3.35 xx 10^(3)` years.