If a radioactive sample has a half-life of 3 years, what fraction remains after 1.5 years?

If a radioactive sample has a half-life of 3 years, what fraction remains after 1.5 years?

• A. 1/4
• B. 1/2
• C. 1/√2
• D. 1/8

Answer: (C)

Radioactive decay is exponential, with the amount remaining given by (1/2)^(t/T_half). Here the half-life is 3 years and the time elapsed is 1.5 years, so t/T_half = 1.5/3 = 0.5. That makes the remaining fraction (1/2)^(0.5) = 1/√2, about 0.707 of the original. intuitively, after halfway to the next half-life, you’re at the square root of the remaining amount.

Radioactive decay is exponential, with the amount remaining given by (1/2)^(t/T_half). Here the half-life is 3 years and the time elapsed is 1.5 years, so t/T_half = 1.5/3 = 0.5. That makes the remaining fraction (1/2)^(0.5) = 1/√2, about 0.707 of the original. intuitively, after halfway to the next half-life, you’re at the square root of the remaining amount.