A piece of radioactive material contains 1000 atmos. If its half -life is 20seconds, the time taken for 125 atoms to remain is

Analyze the question: We start with 1000 atoms. The half-life is 20 s. We want the time when only 125 atoms remain undecayed.

Concept: In each half-life, the number of remaining atoms is halved:

N = N₀ × (1/2)^n, where n = t / T½ is the number of half-lives.

Solution:

Set N = 125 and N₀ = 1000:

125 = 1000 × (1/2)^n

(1/2)^n = 125/1000 = 1/8

Since 1/8 = (1/2)³, n = 3.

Check by halving step by step:

• After 20 s: 1000 → 500
• After 40 s: 500 → 250
• After 60 s: 250 → 125

Time taken: t = n × T½ = 3 × 20 = 60 seconds

Answer: Option D (60 seconds).

Tip: When the remaining fraction is a power of 1/2, count how many halvings it takes. 1/2 → 1 half-life, 1/4 → 2, 1/8 → 3, 1/16 → 4. Then multiply by the half-life. Option B (40 s) is a common trap: it corresponds to only two half-lives, leaving 250 atoms.