You have 1,312 grams of a radioactive kind of lanthanum. If its half-life is 93 minutes, how much will be left after 279 minutes?
To solve this problem, we can use the formula for radioactive decay:
N(t) = N₀ * (1/2)^(t/h)
Where:
N(t) = the amount of the radioactive substance remaining after time t
N₀ = the initial amount of the radioactive substance
t = elapsed time
h = half-life of the radioactive substance
Given that N₀ (initial amount) = 1,312 grams, h (half-life) = 93 minutes, and t (elapsed time) = 279 minutes, we can substitute these values into the formula:
N(279) = 1,312 * (1/2)^(279/93)
Now, let's calculate the value:
N(279) = 1,312 * (1/2)^(3)
N(279) = 1,312 * (1/8)
N(279) = 164
Therefore, after 279 minutes, there will be 164 grams of the radioactive lanthanum remaining.