A radioactive isotope has a half-life of 4.0 days. If a sample initially contains 120 mg of this isotope, how much of the isotope remains after 12 days?
Show the answer and explanation
Correct answer
A. 15 mg
Principle or equation
The remaining mass after n half-lives is given by m = m0 × (1/2)^n, where n = t / T_half.
Why this answer is correct
Half-life T_half = 4.0 days, time t = 12 days, so n = 12 / 4 = 3 half-lives. Remaining mass = 120 mg × (1/2)^3 = 120 × 1/8 = 15 mg.
Example
If a sample starts with 80 mg and has a half-life of 6 hours, after 18 hours (3 half-lives) the remaining mass is 80 × (1/2)^3 = 10 mg.
This published item includes a stored explanation and passed the platform’s publication workflow. It is independent preparation material, not a claim of an official or recalled examination question.