The half-life of a radioactive isotope of X is 50 years. In a nuclear power plant accident, 1 kg of the X isotope is dispersed into the surroundings of the plant. How much of the X isotope will remain in the surroundings after 150 years?

Correct option is C

Radioactive decay follows the formula:
Where:
· N0=1 kg=1000 gm (initial amount)
· t=150 years (elapsed time)
· T=50 years (half-life)
· N = Remaining mass of the isotope after time t.
Information Booster: 1. After 150 years, the radioactive isotope undergoes three half-lives:
· After the first half-life (50 years): 1000×0.5=500 gm.
· After the second half-life (100 years): 500×0.5=250 gm.
· After the third half-life (150 years): 250×0.5=125 gm.
2. The decay process halves the remaining quantity at each step, and the decay is exponential.
3. Applications:
· Used in nuclear waste management, radiometric dating, and medical isotopes.
· Half-life provides insight into the longevity and environmental impact of radioactive materials.