Answer : The percent of the carbon−14 left is, 0.242 %
Explanation :
This is a type of radioactive decay and all radioactive decays follow first order kinetics.
To calculate the rate constant, we use the formula :
Now we have to calculate the amount left.
Expression for rate law for first order kinetics is given by :
where,
k = rate constant =
t = time taken for decay process = 50000 years
a = initial amount or moles of the reactant = 7 g
a - x = amount or moles left after decay process = ?
Putting values in above equation, we get:
The amount left of carbon-14 = 0.0169 g
Now we have to calculate the percent of the carbon−14 left.
Therefore, the percent of the carbon−14 left is, 0.242 %