Answer:
approximately 1,392 grams
Explanation:
The decay of a radioactive substance can be modeled using the formula:
N(t) = N0 * (1/2)^(t / T)
where:
N(t) is the amount of the substance remaining after time t,
N0 is the initial amount of the substance,
t is the time for which we want to calculate the remaining amount,
T is the half-life of the substance.
Given that you have 44,544 grams of europium and its half-life is 9 years, we can use the formula to calculate the amount remaining after 45 years.
Plugging in the values:
N0 = 44,544 grams
t = 45 years
T = 9 years
N(45) = 44,544 * (1/2)^(45/9)
Now we can calculate N(45):
N(45) = 44,544 * (1/2)^(5)
Using the exponent rule for fractional exponents:
(1/2)^5 = 1/32
N(45) = 44,544 * 1/32
N(45) = 1,392 grams (rounded to the nearest gram)
So, after 45 years, approximately 1,392 grams of europium will be left.