Question

An unstable isotope has a half life of 3 days. How many kg of a 820 kg sample will remain after 6 days?

Answer 1

The amount of the unstable isotope that will remain after 6 days is 205 Kg

We'll begin by calculating the the number of half-lives that has elapsed

Half-life (t½) = 3 days

Time (t) = 6 days

Number of half-lives (n) =?

n = t / t(½)

n = 6 / 3

n = 2

Thue, 2 half-lives has elapsed

• Finally, we shall determine the amount remaining.

Number of half-lives (n) = 2

Original amount (N₀) = 820 Kg

Amount remaining (N) =?

N = 1/2ⁿ × N₀

N = 1/2² × 820

N = 1/4 × 820

N = 0.25 × 820

N = 205 Kg

Thus, 205 Kg of the unstable isotope will remain after 6 days

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