Which statement correctly defines the half-life concept?

Which statement correctly defines the half-life concept?

• A. Remaining activity = initial × (1/2)^n
• B. Remaining activity = initial × 2^n
• C. Remaining activity = initial ÷ n
• D. Remaining activity = initial × (1/3)^n

Answer: (A)

The essential idea is that each half-life halves the amount that remains. If you start with an initial activity A0, after n half-lives the activity becomes A0 × (1/2)^n. This expression captures the exponential decay: every passing half-life multiplies the remaining activity by 1/2, so it drops rapidly in steps of halves. For example, with A0 = 100 Bq, after one half-life you have 50 Bq, after two you have 25 Bq, and after three you have 12.5 Bq, and so on. The other forms don’t reflect this halving pattern. Using initial × 2^n would increase with each half-life, which isn’t what happens. Dividing by n isn’t tied to the fixed halving intervals, so it wouldn’t describe exponential decay. Using (1/3)^n would imply the remaining activity drops by thirds each time, not by halves.

The essential idea is that each half-life halves the amount that remains. If you start with an initial activity A0, after n half-lives the activity becomes A0 × (1/2)^n. This expression captures the exponential decay: every passing half-life multiplies the remaining activity by 1/2, so it drops rapidly in steps of halves. For example, with A0 = 100 Bq, after one half-life you have 50 Bq, after two you have 25 Bq, and after three you have 12.5 Bq, and so on.

The other forms don’t reflect this halving pattern. Using initial × 2^n would increase with each half-life, which isn’t what happens. Dividing by n isn’t tied to the fixed halving intervals, so it wouldn’t describe exponential decay. Using (1/3)^n would imply the remaining activity drops by thirds each time, not by halves.