Calculate the decay constant of a radioactive isotope of half-life 138.5 s.

Analyze the question: We're given the half-life (T½ = 138.5 s) and asked for the decay constant (λ).

Concept: The half-life and decay constant are related by:

λ = ln 2 / T½ = 0.693 / T½

Solution:

λ = 0.693 / 138.5

Since 138.5 × 0.005 = 0.6925, we get:

λ ≈ 0.693 / 138.5 ≈ 5.004 × 10⁻³ s⁻¹

Using ln 2 = 0.6931 gives 0.6931 / 138.5 = 5.0043 × 10⁻³ s⁻¹, which rounds to 5.0 × 10⁻³ s⁻¹.

Checking the options:

• A. 5.0 × 10⁻³ s⁻¹ matches our result.
• B, C and D are off by about 2% or more, so they don't fit.

Tip: JAMB often picks half-life values that make the arithmetic neat. When you see 138.5 s, think "0.693 ÷ 138.5 = 0.005". Numbers like 138.6 (= 100 × 1.386) or 69.3 are strong hints that the answer is a round figure. Always remember λ = 0.693 / T½, and check that your units are s⁻¹.