Question

A certain radioisotope has a half-life of 8.0 hours; how much of a 192 g sample of this radioisotope would decay after a full day?

Answer 1

If the half-life is 8.0 hours and there are 24 hours in a day, the radioisotope reaches its half-life 3 times.

Therefore, after a full day, there are 24 g of the sample left, and 168 g has decayed.

Answer 2

Answer:

167.9895 grams sample of this radioisotope would decay after a full day.

Explanation:

$N=N_o\times e^{-\lambda t}$

$\lambda =\frac{0.693}{t_{1/2}}$

$N_o$ = initial amount of radioisotope

N = Amount of radioisotope left after time t.

$\lambda$ = Decay Constant

$t_{1/2}$ = Half life of the radioisotope

We have:

$N_o=192 g$

$t_{1/2}=8.0 hours$

t = 1 day = 24 hour

$\lambda =\frac{0.693}{8.0 hour}=0.086625 hour^{-1}$

$N=192 g\times e^{-0.086625 hour^{-1}\times 24 hours}$

N = 24.0105 g

24.0105 grams of radioisotope will remain after 1 whole day.

Amount of radioisotope decayed = $N_o-N=192 g- 24.0105 g=167.9895 g$

167.9895 grams sample of this radioisotope would decay after a full day.