The half life of a radioactive element is 140 days. After 560 days, one gram of the element will be reduced to:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0.0625 g
Core Concept
Radioactive decay follows:
N = N₀ (1/2)ⁿ
Where
(N): The remaining amount (or number) of the radioactive substance.
(N°): The initial amount (or number) of the radioactive substance.
(n): The number of half-lives that have elapsed.
(1/2)ⁿ: The fraction of the sample remaining.
Stepwise Calculation
Half-life = 140 days
Total time = 560 days
Number of half lives
n = 560 / 140
n = 4
Amount remaining
N = 1 × (1/2)⁴
N = 1 × (1/16)
N = 0.0625 g