Question

Analyzing a Radioactive Decay Curve
A graph titled radioactive decay of isotope X with time in seconds on the x-axis from 0 to 200 and number of radioactive atoms on the y-axis from 0 to 120. There is a curve with the following points (0, 100), (25, 50), (50, 25), (75, 15), (100, 8), (125, 5), (150, 3) and (175, 1).

Use the graph to answer the questions.



What is the half-life of isotope X?

How many radioactive atoms of isotope X are left after 3 half-lives?

How many half-lives must have occurred if only 7 atoms of isotope X are left?

Answer 1

1. Half-life = 25 s (100 → 50 in 25 s).

2. After 3 half-lives: 100 × (1/2)^3 = 100/8 = 12.5 atoms (≈ 13 atoms).

3. Solve 100 × (1/2)^n = 7 → (1/2)^n = 0.07 → n = log(0.07)/log(0.5) ≈ 3.84 half-lives.
(That corresponds to a time ≈ 3.84 × 25 s ≈ 96 s; roughly 4 half-lives.)