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

1 answer

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.