Asample taken from a layer of mica in a canyon has 2.10 grams of potassium-40. a test reveals it to be 2.6 billion years old. how much potassium-40 was in the sample originally if the half-life of potassium-40 is 1.3 billion years? a. 4.20 g b. 8.40 g c. 12.6 g d. 16.8 g e. 25.2 g

Answer : The correct option is, (B) 8.40 g

Solution : Given,

As we know that the radioactive decays follow the first order kinetics.

First, we have to calculate the half life of a potassium-40.

Formula used :

Now put the value of half-life, we get the value of rate constant.

The expression for rate law for first order kinetics is given by :

where,

k = rate constant  =

t = time taken for decay process  =

a = initial amount of potassium-40 = ?

a - x = amount left after decay process  = 2.10 g

Now put all the values in above equation, we get

Therefore, the amount of potassium-40 in the sample originally was, 8.40 g

The correct answer is option B.

Explanation:

Initial amount of an isotope =

Final amount of an isotope = N

Half life of an isotope =

Hence, the correct answer is option B.