A sample of the igneous intrusion within the outcrop has 1682 Potassium-40 atoms, and 318 Argon-40 atoms. How old is the igneous intrusion

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

your answer would be a. 12.5 kg