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?
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.