Will you check this answer for me?
the half-life of strontium-87 is 2.8hr. What percentage of this isotope will remain after 8 hours and 24 minutes?
?? 34%
I'd be interested in knowing how you came up with that answer.
8 hr and 24 min, according to my calculation is [(8*60)+24/60] = 8.4 hrs.
k = 0.693/t1/2 = 0.693/2.8 = 0.2475
ln(No/N) = kt
I took No = 100 (an arbitrary number)
Solved for N
k from above
t = 8.4
Solving for N, I obtained 12.5 so if we started with 100 g at time = zero, then at the end of 8.4 hours we would have 12.5 g left. %left = (12.5/100)*100 = ??
Check my work.
To determine the percentage of strontium-87 that remains after 8 hours and 24 minutes, we need to use the concept of half-life.
The half-life of strontium-87 is 2.8 hours, which means that after every 2.8 hours, half of the initial amount of strontium-87 will decay.
First, let's convert 8 hours and 24 minutes to hours. There are 60 minutes in an hour, so 24 minutes is equal to 24/60 = 0.4 hours. Therefore, the total time is 8 + 0.4 = 8.4 hours.
Now, let's calculate how many times the half-life of strontium-87 occurs within the given time period. Divide the total time (8.4 hours) by the half-life (2.8 hours):
8.4 hours / 2.8 hours = 3
So, within the given time period, the half-life of strontium-87 occurs three times.
Since each half-life results in a 50% decay, we can calculate the remaining percentage of strontium-87 by taking 50% (for each half-life) to the power of the number of half-lives (3 in this case):
Percentage remaining = (1/2)^n
Where n is the number of half-lives.
Percentage remaining = (1/2)^3 = 1/8 = 0.125
Converting this to a percentage gives us 0.125 * 100 = 12.5%.
Therefore, after 8 hours and 24 minutes, 12.5% of the strontium-87 isotope will remain, not 34%.
To check the answer, we can use the formula for calculating the remaining amount of a radioactive substance after a certain amount of time.
The formula is:
Remaining = Initial * (1/2)^(t/h)
In this case, the initial amount is 100% (or 100), since we are dealing with the percentage of the isotope.
t represents the time that has passed, which in this case is 8 hours and 24 minutes. We need to convert this time to hours by dividing minutes by 60 and adding it to the hours.
t = 8 + 24/60 = 8.4 hours
h represents the half-life, which is given as 2.8 hours.
Now we can substitute these values into the formula:
Remaining = 100 * (1/2)^(8.4/2.8) = 100 * (1/2)^3 = 100 * (1/8) = 12.5%
So, after 8 hours and 24 minutes, approximately 12.5% of the strontium-87 isotope will remain. Therefore, the answer provided (34%) is not accurate.