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Trava [24]
3 years ago
10

A certain radioactive isotope has leaked into a small stream. Three hundred days after the​ leak, 3% of the original amount of t

he substance remained. Determine the​ half-life of this radioactive isotope.
Mathematics
1 answer:
sesenic [268]3 years ago
6 0
If the half-life is t, then every t days, the amount of the radioactive isotope will be cut in half.
(1/2)^(number of half-lives) = 3%
number of half-lives = ln(0.03) / ln(0.5)
This gives the number of half-lives as 5.06.
Then 300 days = (5.06)(length of 1 half-life)
length of 1 half-life = 300 / 5.06 = 59.29 days
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