3.

A rock sample contains 80g of a potassium-40

(K10) isotope with a half-life of 1.25 billion years.

How much of the potassium-40 isotope will remain

after 2.5 billion years have passed?

A. Og

B. 10g

C. 20g

D. 80g

20 g

Explanation:

We are given;

Original mass of K-40 before decay = 80 g

Half life of Potassium-40 = 1.25 billion years

Time taken by the decay = 2.5 billion years

We are required to calculate the mass of K-10 that will remain after 2.5 billion years.

Using the formula;

Remaining mass = Original mass * (1/2) ^n

where n is the number of half lives

Number of half lives, n = Time taken : half-life

= 2.5 billion years : 1.25 billion years

= 2

Remaining mass = 80 g * (0.5) ^2

= 80 g * 0.25

= 20 g

Therefore, the mass of K-40 isotope that will remain after 2.5 billion years is 20 g.