Answer to Question #348629 in General Chemistry for Meg

Question

The isotope strontium-90 is produced during the testing of nuclear weapons. If 100.0mg of strontium-90 was released in the atmosphere in 1960, how much of the radioisotope remains 85 years later? The half-life of strontium-90 is 29 years. Show all your work.

Answer 1

Solution:

Strontium-90 ⇨ Sr-90

The half-life (t_1/2) of strontium-90 is 29 years

From law of radioactive decay:

t_1/2 = ln(2) / λ

where λ = decay constant

λ = ln(2) / t_1/2

λ = (0.693) / (29 years) = 0.0239 years⁻¹

Radioactive decay follows the kinetics of a first order reaction:

ln[Sr-90]_t = −λt + ln[Sr-90]_o

 

λ = 0.0239 years⁻¹

t = 85 years

[Sr-90]_o = 100.0 mg

[Sr-90]_t = unknown

Therefore,

ln[Sr-90]_t = −(0.0239 years⁻¹ × 85 years) + ln(100.0)

ln[Sr-90]_t = −2.0315 + 4.60517 = 2.57367

[Sr-90]_t = e^2.57367 = 13.11

[Sr-90]_t = 13.11 mg

Answer: 13.11 mg of the radioisotope (Sr-90) remained