Half-life halves the number of radioactive atoms every fixed period

Steps:

• Half-life is 12 years, so 24 years equals 2 half-lives.
• After 1 half-life, atoms remaining: 40 million / 2 = 20 million.
• After 2 half-lives, atoms remaining: 20 million / 2 = 10 million.
• Formula: N = N0 × (1/2)^t/T, where t=24, T=12, so (1/2)^2 = 1/4, 40 million / 4 = 10 million.

Why B is correct:

• Half-life definition: exactly half the atoms decay per half-life period, so after two half-lives, 1/4 remain.

Why the others are wrong:

• A: Matches after one half-life (12 years), not two.
• C: Matches after three half-lives (36 years).
• D: Radioactive decay approaches zero asymptotically but never reaches exactly zero.

Final answer: B