Answer:
Step-by-step explanation:
To determine the time it takes for a radioactive sample to decay to a specific amount, we can use the radioactive decay formula:
N(t) = N₀ * (1/2)^(t / t₁/₂)
Where:
N(t) is the remaining amount of the radioactive substance at time t
N₀ is the initial amount of the radioactive substance
t is the time that has passed
t₁/₂ is the half-life of the substance
In this case, the initial amount of the sample is 560g, and we want to find the time it takes for it to decay to 140g.
Using the formula, we can rearrange it to solve for time (t):
t = t₁/₂ * log₂(N₀ / N(t))
Plugging in the values:
t = 0.025 * log₂(560 / 140)
t ≈ 0.025 * log₂(4)
Using the logarithmic property log₂(a) = log(a) / log(2):
t ≈ 0.025 * (log(4) / log(2))
t ≈ 0.025 * 2
t ≈ 0.05 seconds
Therefore, it will take approximately 0.05 seconds for a 560g sample of hafnium-156 to decay to 140g.