Question

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?

Answer 1

Answer:

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.