How long will it take for the radiation level of strontium-85 to drop to one-sixteenth of its original level?
Express your answer as an integer.
The decay of a radioactive substance can be modeled using the formula N = N0 * (1/2)^(t/h), where N is the current amount, N0 is the initial amount, t is the time elapsed, and h is the half-life of the substance.
For strontium-85, the half-life is 64.84 days. To find the time it takes for the radiation level to drop to one-sixteenth of its original level, we need to find t when N/N0 = 1/16.
1/16 = (1/2)^(t/h)
Taking the logarithm of both sides, we get:
log(1/16) = log((1/2)^(t/h))
log(1/16) = (t/h) * log(1/2)
Solving for t, we divide both sides by log(1/2):
t/h = log(1/16) / log(1/2)
Using the change of base formula, we can rewrite log(1/16) / log(1/2) as log base 2 of 1/16:
t/h = log2(1/16)
Using properties of logarithms, we can simplify further:
t/h = log2(2^-4)
t/h = -4 * log2(2)
t/h = -4 * 1
t/h = -4
Therefore, it would take exactly 4 half-lives for the radiation level of strontium-85 to drop to one-sixteenth of its original level.
Since each half-life is 64.84 days, the total time it would take is 4 * 64.84 = 259.36 days.
However, since we are asked to express the answer as an integer, the closest whole number is 259.
The time it takes for the radiation level of a radioactive substance to decrease to one-sixteenth of its original level can be calculated using the concept of half-life. The half-life of strontium-85 is 64.8 days.
To find the time it takes for the radiation level to drop to one-sixteenth, we need to determine how many half-lives are required.
The formula to calculate the number of half-lives is:
Number of half-lives = (log(Base 2) of (original level/final level))
Using this formula, the calculation becomes:
Number of half-lives = log₂(1/16) = -4
Since we are looking for the time it takes, we need to multiply the number of half-lives by the half-life of strontium-85:
Time = Number of half-lives * Half-life = -4 * 64.8 days = -259.2 days ≈ -259 days
Expressing the answer as an integer, it will take approximately 259 days for the radiation level of strontium-85 to drop to one-sixteenth of its original level.