Answer: the igneous intrusion is 325 million years old
Explanation:
In the sample of the igneous intrusion
Number of Potassium-40 atoms (parent atom) = 1682
Number of Argon-40 atoms (daughter atom) = 318
Half-life of the Potassium40- Argon40 radioactive pair = 1.3 billion years = 1.3 × 10⁹ years
We now want to know the absolute age of the igneous intrusion.
At t = 0
i.e. when the igneous intrusion took place there will be no daughter atom (Ar-40).
So the number of parent (K-40) will be 1682 + 318 = 2000 atoms
Total number of atoms = parent + daughter = 2000 + 0 = 2000
Now after a given time
Number of Parent atom (K-40) = 1682
Number of Daughter atom (Ar-40) = 318
percent of parent atom (K-40)
= (Number of parent atom / total number of atoms) × 100
= (1682/2000) × 100
= 84.1 %
percentage of daughter atom (Ar-40) = 100 - % of K-40 atoms
= 100 – 84.1
= 15.9 %
Now from the table of “decay parameters for all radioactive decay pairs” which is uploaded along this answer
When Parent atom = 84.1 % and daughter atom = 15.9 %
then Age is given as 0.250T_1/2
THEREFORE age of the igneous intrusion
= 0.250 × 1.3 × 10⁹ years
= 0.325 × 10⁹ years
= 325 million years.
SO the igneous intrusion is 325 million years old
