Question

The half life of an isotope is 20 minutes. After 2.00 hours, 0.10 grams of the sample remains. how many grams was in the original sample.?

Answer 1

The half life of a radioactive isotope is 20 minutes, i.e, t_1/2 = 20 min. Therefore, the radiactive decay constant is λ = 0.693/t_1/2 = 0.693/(20 min).

The time taken for the radio isotope to decay to 0.10 g is 2.00 hour = (2.00 h)*(60 min/1 h) = 120 min.

Let N₀ = initial amount of the radio isotope and N_t = 0.10 g is the amount remaining after t = 120 min.

Use the radioactive decay law.

ln N_t/N₀ = -λ*t

Plug in values and get

ln (0.10 g/N₀) = -(0.693/20 min)*(120 min) = -(0.693)*6 = -4.158

===> (0.10 g/N₀) = e^(-4.158)

===> (0.10g/N₀) = 0.01564

===> N₀ = (0.10 g/0.01564) = 6.3939 g ≈ 6.40 g.

The amount of the radioactive isotope originally present is 6.40 g (ans).