Question

Stronitum-90 has a half-life of 29 years. If a site held 2000 kg of this isotope, approximately what mass of strontium-90 would be left after 116 years?

A. 250 kg
B. 1000 kg
C. 300 kg
D. 125 kg
E. 500 kg

Answer 1

To find the remaining mass of strontium-90 after 116 years, we halve the initial mass for each 29-year half-life interval. After four half-lives (116 years), the remaining mass is 125 kg.

Step-by-step explanation:

To calculate the mass of strontium-90 remaining after 116 years, we use the fact that after each half-life period, the amount of the radioactive substance reduces by half. Strontium-90 has a half-life of 29 years. To find out how many half-lives 116 years constitute, we divide 116 by the half-life: 116 years / 29 years/half-life = 4 half-lives.

Starting with 2000 kg, we halve the amount for each half-life:

• After 1 half-life (29 years): 1000 kg
• After 2 half-lives (58 years): 500 kg
• After 3 half-lives (87 years): 250 kg
• After 4 half-lives (116 years): 125 kg

Therefore, approximately 125 kg of strontium-90 would remain after 116 years.