The relationship between the decay constant (λ) and the half-life (T½) is:

Correct answer: (c) T½ = 0.693/λ

Explanation

In radioactive decay, N = N₀e^(−λt). The half-life is the time in which half the nuclei decay, so N = N₀/2:

• ½ = e^(−λT½), so λT½ = ln 2 ≈ 0.693;
• T½ = 0.693/λ.

So the half-life is inversely proportional to the decay constant: a substance that decays faster (larger λ) has a shorter half-life. Carbon-14, for example, has a half-life of about 5,730 years.