Answer : The age of the rock is, 2.60 billion years
Explanation :
Half-life = 1.3 billion years
First we have to calculate the rate constant, we use the formula :
Now we have to calculate the time passed.
Expression for rate law for first order kinetics is given by:
where,
k = rate constant =
t = time passed by the sample = ?
a = initial amount of the reactant = 12 mg
a - x = amount left after decay process = 3 mg
Now put all the given values in above equation, we get
Therefore, the age of the rock is, 2.60 billion years