To solve this problem, we can use the formula for exponential decay:
\[ N(t) = N_0 * (1/2) ^ {t/T} \]
where:
N(t) = final amount of actinium after time t
N0 = initial amount of actinium
t = time elapsed
T = half-life of actinium
Plugging in the values given:
N0 = 48 grams
T = 22 years
t = 88 years
\[ N(t) = 48 * (1/2) ^ {88/22} \]
\[ N(t) = 48 * (1/2) ^ 4 \]
\[ N(t) = 48 * (1/16) \]
\[ N(t) = 3 \]
Therefore, after 88 years, only 3 grams of actinium will be left.
The half-life of a radioactive kind of actinium is 22 years. If you start with 48 grams of it, how much will be left after 88 years?
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