Antinium-226 has a half life of 29 hours. If 80 mg of antinium-226 disintegrates over a period of 87 hours, how many mg of antinuim– 226 will remain?
7.25 mg
10 mg
21.75 mg
20 mg
To solve this problem, we can use the formula for exponential decay:
N(t) = N₀ * (1/2)^(t / h)
Where:
- N(t) represents the remaining amount of antinium-226 at time t
- N₀ represents the initial amount of antinium-226
- h represents the half-life of antinium-226
In this case, N₀ = 80 mg, t = 87 hours, and h = 29 hours. Plugging these values into the formula, we get:
N(87) = 80 * (1/2)^(87 / 29)
Simplifying the exponent, we have:
N(87) ≈ 80 * (1/2)^3 ≈ 80 * (1/8) ≈ 10 mg
Therefore, approximately 10 mg of antinium-226 will remain after 87 hours.
So the answer is 10 mg.