Answer:
167.9895 grams sample of this radioisotope would decay after a full day.
Explanation:
[tex]N=N_o\times e^{-\lambda t}[/tex]
[tex]\lambda =\frac{0.693}{t_{1/2}}[/tex]
[tex]N_o[/tex] = initial amount of radioisotope
N = Amount of radioisotope left after time t.
[tex]\lambda [/tex] = Decay Constant
[tex]t_{1/2}[/tex] = Half life of the radioisotope
We have:
[tex]N_o=192 g[/tex]
[tex]t_{1/2}=8.0 hours[/tex]
t = 1 day = 24 hour
[tex]\lambda =\frac{0.693}{8.0 hour}=0.086625 hour^{-1}[/tex]
[tex]N=192 g\times e^{-0.086625 hour^{-1}\times 24 hours}[/tex]
N = 24.0105 g
24.0105 grams of radioisotope will remain after 1 whole day.
Amount of radioisotope decayed = [tex]N_o-N=192 g- 24.0105 g=167.9895 g[/tex]
167.9895 grams sample of this radioisotope would decay after a full day.
