The radioactive element thorium-234 has a half-life of approximately 24 days. If I started with 82 grams of it, how much thorium would remain after 96 days?

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Answer 1 · 2018-06-05T05:42:28

$5.125 g$ $"5.125 g"$

If $96$ $96$ days is $n$ $"n"$ half lives then

$n = \frac{96 days}{24 days/half life} = 4 half lives$ $"n" = "96 days"/("24 days/half life") = "4 half lives"$

Amount of radioactive substance left after $n$ $"n"$ half lives is given by

$N_{t} = \frac{N_{0}}{2^{n}}$ $"N"_t = "N"_0/(2^"n")$

Where

$N_{t} = \frac{82 g}{2^{4}}$ $"N"_t = "82 g"/2^4$

$N_{t} = \frac{82 g}{16}$ $color(white)("N"_t) = "82 g"/16$

$N_{t} = 5.125 g$ $color(white)("N"_t) = "5.125 g"$