In 90 seconds, the mass of a radioactive element reduces to $\frac{1}{16}$ of its original value. Determine the half- life of the element.

Analyze the question: The mass drops to 1/16 of its original value in 90 s. We need the half-life, which is the time for the mass to fall to half.

Concept: After n half-lives, the fraction remaining is (1/2)ⁿ.

Solution:

1. Set (1/2)ⁿ = 1/16
2. Since 16 = 2⁴, we get (1/2)ⁿ = (1/2)⁴, so n = 4 half-lives
3. Total time = n × T½ 90 s = 4 × T½ T½ = 90 ÷ 4 = 22.5 s

Check: 22.5 s → 1/2, 45 s → 1/4, 67.5 s → 1/8, 90 s → 1/16 ✓

Tip: For problems like this, count how many times you halve to reach the given fraction (1 → 1/2 → 1/4 → 1/8 → 1/16 is 4 halvings). Then divide the total time by that number. Watch out for option E (45 s): it would be correct only if the mass dropped to 1/4 in 90 s.