Thulium-167 has a half life of 9.0 days. If the initial amount of thulium is 50.0 grams. How many grams are left after 36.0 days?

3.125 grams.

Explanation:

It is known that the decay of a radioactive isotope isotope obeys first order kinetics. Half-life time is the time needed for the reactants to be in its half concentration. If reactant has initial concentration [A₀], after half-life time its concentration will be ([A₀]/2). Also, it is clear that in first order decay the half-life time is independent of the initial concentration.

∵ Thulium-167 has a half life of 9.0 days.

∴ The time is needed to calculate the grams are left after (36.0 days) represents (36.0 days / 9.0 days) = 4.0 half-lives.

50.0 grams → (first half life) 25.0 grams → (second half life) 12.5 grams → (third half life) 6.25 grams → (fourth half life) 3.125 grams.

So, the grams are left after 36.0 days = 3.125 grams.