Strontium-85, used for bone scans, has a half-life of 64 {\rm d}.How long will it take for the radiation level of strontium-85 to drop to \frac{1}{8} of its original level?
I assume the half life is 64 days and you want to reduce the radiation to 1/8 of its original value.
k = 0.693/t1/2 and substitute this into the below equation.
ln(No/N) = kt.
No = 100 (an arbitrary number I picked).
N = 12.5 (100/8) = 12.5
k from above.
Solve for t in days.
To solve this problem, we can use the concept of half-life. The half-life of an isotope is the time it takes for half of the atoms in a sample to decay.
Given that the half-life of strontium-85 is 64 days, and we want to find out how long it takes for the radiation level to drop to 1/8 (or 1/2^3) of its original level. Let's break down the problem step by step:
Step 1: Determine the number of half-lives required to reach the desired level.
Since we want the radiation level to drop to 1/8 of its original level, this corresponds to 3 half-lives. This is because 2^3 (2 to the power of 3) is equal to 8.
Step 2: Calculate the total time.
To find the total time required, we multiply the half-life by the number of half-lives. In this case, we multiply 64 days (the half-life) by 3 (the number of half-lives):
Total time = 64 days * 3 = 192 days.
So, it will take 192 days for the radiation level of strontium-85 to drop to 1/8 of its original level.
To determine how long it will take for the radiation level of strontium-85 to drop to 1/8 of its original level, we can use the concept of half-life.
The half-life refers to the time it takes for half of a radioactive substance to decay. In this case, we're given that strontium-85 has a half-life of 64 days.
To find the time it takes for the radiation level to drop to 1/8 of its original level, we need to calculate how many half-lives are needed to reach this point.
Since 1/8 is less than 1/2, we know that it will take more than one half-life for the radiation level to decrease to this amount.
Let's break it down step by step:
1. Determine the number of half-lives needed to reach 1/8 level:
To find this, we can use the following formula:
Number of half-lives = (log(final level/initial level)) / (log(1/2))
Here, the "final level" is 1/8 (or 1/2^3) and the "initial level" is 1 (or 1/2^0). So, we have:
Number of half-lives = (log(1/2^3) / log(1/2))
2. Calculate the time needed for the radiation level to drop to 1/8:
Since each half-life is 64 days, we can multiply the number of half-lives by the half-life period:
Time needed = (Number of half-lives) × (Half-life period)
To summarize, follow these steps:
1. Calculate the number of half-lives using the given formula.
2. Multiply the number of half-lives by 64 days to find the total time needed.
(Note: For the mathematical calculations, log refers to the logarithm, and log(1/2) refers to the logarithm base 10 for 1/2.)