If you have 10 grams of a substance that decays with a half-life of 14 days, then how much will you have after 70 days?

a. 0.31 g

b. 0.10 g

c. 2.50 g

d. 1.25 g

a. 0.31 g

Explanation:

It is known that the decay of a radioactive isotope isotope obeys first order kinetics. Also, it is clear that in first order decay the half-life time is independent of the initial concentration. 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). The half-life time of the substance = 14 days.

So, 70 days represent (70 days / 14 days = 5.0 half-lives).

So, the substance will decay:

10 g → (first half-life = 14 days) 5 g → (second half-life = 28 days) 1.5 g → (third half-life = 42 days) 1.25 g → (fourth half-life = 56 days) 0.625 g → (fifth half-life = 70 days) 0.3125 g.

So, the right choice is: a. 0.31 g.