The half-life of radon-222 is 3.8 days. How much of a 300 gram sample is left after 14.8
days?
300*(1/2)^(14.8/3.8) = 20.17 g
To calculate how much of a sample is left after a certain amount of time has passed, we can use the formula for exponential decay:
N(t) = N₀ * (1/2)^(t / t₁/₂)
Where:
N(t) is the amount of the sample remaining after time t,
N₀ is the initial amount of the sample,
t is the elapsed time, and
t₁/₂ is the half-life of the substance.
In this case, the initial amount of the sample (N₀) is 300 grams, the elapsed time (t) is 14.8 days, and the half-life (t₁/₂) of radon-222 is 3.8 days.
Substituting the values into the formula, we get:
N(14.8) = 300 * (1/2)^(14.8 / 3.8)
To solve this equation, we can calculate the right side of the equation first, then multiply it by the initial amount of the sample (300 grams).
Let's calculate the right side of the equation using a calculator or a computer program:
(1/2)^(14.8 / 3.8) ≈ 0.19233
Now we can substitute this value back into the equation:
N(14.8) ≈ 300 * 0.19233
By multiplying these two values, we find that approximately 57.7 grams of the sample is left after 14.8 days.