Question

Strontium-90 is one of the products of the fission of uranium-235. This strontium isotope is radioactive, with a half-life of 28.1 yr. Calculate how long it will take for 0.900 g of the isotope to be reduced to 0.170 g by decay.

Answer 1

Answer:

67.6 years is the time the isotope take to decay from 0.900g to 0.170g

Explanation:

The radioactive decay follows first order law:

Ln [A] = -kt + ln[A]₀

Where [A] is concentration after time t,

k is decay constant:

k = ln 2 / t(1/2)

k = ln2 / 28.1 years

k = 0.02467 years⁻¹

[A]₀ = Initial concentration.

We can replace concentration and use the mass of the isotope:

Ln [A] = -kt + ln[A]₀

Ln [0.170g] = -0.02467 years⁻¹t + ln[0.900g]

-1.667 = -0.02467 years⁻¹t

t =

67.6 years is the time the isotope take to decay from 0.900g to 0.170g