In 24 days a radioactive isotope decreases in mass from 128g to 2g. What is the half-life of the radioactive material?

Analyze the question: A radioactive isotope decays from 128 g to 2 g in 24 days. We need the half-life.

Concept: In each half-life, the mass of the radioactive substance is halved:

N = N₀ × (1/2)ⁿ, where n = number of half-lives = total time ÷ half-life.

Solution:

1. Find the fraction remaining: 2/128 = 1/64

2. Express 1/64 as a power of 1/2: 1/64 = (1/2)⁶, so n = 6

Check by halving: 128 → 64 → 32 → 16 → 8 → 4 → 2. That is 6 halvings.

3. Find the half-life: n = total time ÷ T½ 6 = 24 ÷ T½ T½ = 24 ÷ 6 = 4 days

Answer: The half-life is 4.00 days, which is option B.

Tip: For half-life problems, halve the mass step by step and count the steps. That count is n, and then T½ = total time ÷ n. Also remember that 2⁶ = 64 and 2⁷ = 128, which helps you spot the number of halvings quickly.