The half life of a radioactive element is 140 days. After 560 days, one gram of the element will be reduced to:

0.0625 g

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