In the early 1960s, radioactive strontium-90 was released during atmospheric testing of nuclear weapons and got into the bones of people alive at the time. If the half-life of strontium-90 is 32 years, what fraction of the strontium-90 absorbed in 1965 remained in people's bones in 1996?
1996 is 31 years after 1965. Since the half life is 32 years, the amount of Sr-90 is nearly, but not quite, reduced by half.
Fot the exact number,
N/No = 2^(-31/32) = 0.511
To determine the fraction of strontium-90 that remained in people's bones from 1965 to 1996, we need to calculate the number of half-lives that occurred during this period.
The half-life of strontium-90 is 32 years, which means that every 32 years, the amount of strontium-90 is reduced by half.
To find the number of half-lives, we can subtract the starting year (1965) from the ending year (1996) and divide it by the half-life (32 years).
1996 - 1965 = 31 years
31 years ÷ 32 years = 0.96875
So, approximately 0.96875 half-lives occurred between 1965 and 1996.
To calculate the fraction remaining, we raise the fraction 0.5 (representing the amount reduced by half in each half-life) to the power of the number of half-lives (0.96875).
Fraction remaining = 0.5 ^ 0.96875 ≈ 0.56096
Therefore, approximately 0.56096, or 56.1% (rounded to one decimal place), of the strontium-90 absorbed in 1965 remained in people's bones in 1996.
To determine the fraction of strontium-90 absorbed in 1965 that remained in people's bones in 1996, we need to calculate the number of half-lives that have passed from 1965 to 1996, and then use that to find the fraction remaining.
The half-life of strontium-90 is given as 32 years. A half-life is the amount of time it takes for half of the radioactive material to decay.
To calculate the number of half-lives that have passed from 1965 to 1996, we need to find the time difference between these two years.
1996 - 1965 = 31 years
Now, we divide this time difference by the half-life of strontium-90:
31 years / 32 years = 0.96875
This result tells us that approximately 0.96875 of a half-life has passed.
To find the fraction remaining, we use the following formula:
Fraction remaining = (1/2)^(number of half-lives)
Plugging in the calculated number of half-lives:
Fraction remaining = (1/2)^(0.96875)
Now we can calculate this fraction remaining:
Fraction remaining ≈ 0.526
Therefore, approximately 52.6% of the strontium-90 absorbed in 1965 remained in people's bones in 1996.