Question

You are provided a 200g sample of potassium chloride (KCl) that contains natural potassium. How many atoms of 40K will exist in the sample after 1,000,000,000 years?

Answer 1

The half life of potassium 40K is 1.251 x 10⁹ years

The number of moles of potassium in 200 g = 200 / 40 = 50 moles

Each mole has 6.022 x 10²³ atoms , so 50 moles will have 50 x 6.022 x 10²³ = 3.011 x 10²⁵ atoms

So using the formula :

Nt = No (1/2)^{t / t 0.5}

where Nt is the amount of atoms left after time t

no is the initial number of atoms

t is the time lapsed

t 0.5 is the half life

putting the values we get

Nt = 3.011 x 10²⁵ (1/2)^{10^9 / 1.251 x 10^9}

Nt = 1.73 x 10²⁵ atoms

So the number of 40K atoms left after 1,000,000,000 years will be 1.73 x 10²⁵.