You have 11.20 grams of a compound. It is known that the compound has a half-life of 3.8 days. How long will it take for the compound to decay to 0.350 grams?
How many half lives does it go through?
# half lives x 3.8 days/half life = ? days.
To determine how long it will take for the compound to decay to 0.350 grams, we can use the equation for exponential decay:
N(t) = N₀ * (1/2)^(t/h)
Where:
N(t) is the final amount of the compound (0.350 grams)
N₀ is the initial amount of the compound (11.20 grams)
t is the time it takes for the decay to occur (in days)
h is the half-life of the compound (3.8 days)
We can rearrange the equation to solve for t:
t = h * log₂(N(t)/N₀)
Now let's calculate the time it will take:
t = 3.8 * log₂(0.350/11.20)
Using a calculator or logarithmic table, we find:
t ≈ 28.24 days
Therefore, it will take approximately 28.24 days for the compound to decay to 0.350 grams.