Question

A radioactive sample has a half life of 1 hour. If you start with 1.000 gram of it at noon, how much of it remains at 4pm

Answer 1

The amount of the sample remaining at 4pm is 0.0625 g

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

Half-life (t½) = 1 hour

Time (t) = 4 hour

Number of half-lives (n) =?

n = t / t½

n = 4 / 1

n = 4

• Finally, we shall determine the amount the sample remaining at 4pm

Number of half-lives (n) = 4

Initial amount (N₀) = 1 g

Amount remaining (N) =?

$N = \frac{N_0}{ {2}^{n}} \\ \\ N = \frac{1}{ {2}^{4}} \\ \\ N = \frac{1}{16} \\ \\ N = 0.0625 \: g$

Thus, the amount remaining at 4pm is 0.0625 g

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