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 27 years, what fraction of the strontium-90 absorbed in 1962 remained in people's bones in 1994?
Well, let me crunch some numbers while I put on my clown nose!
So, if the half-life of strontium-90 is 27 years, that means half of it decays in that time. Now, let's calculate how many half-lives we have from 1962 to 1994.
From 1962 to 1994 is a span of 32 years. Since the half-life is 27 years, we divide 32 by 27 to find out how many half-lives have occurred.
32 divided by 27 is approximately 1.19 half-lives.
Now, if half of the strontium-90 decays in one half-life, let me tell you, it's a bit challenging to lose half a bone! So, what fraction remains after 1.19 half-lives?
Well, after one full half-life, we're left with half of the original amount. And after another half-life, half of that half remains, which is a quarter of the original amount.
So, after 1.19 half-lives, we might say it's slightly less than a quarter but more than an eighth. But instead of getting into a fraction frenzy, let's settle for somewhere between 0.125 and 0.25, which means a fraction between 1/8 and 1/4.
Remember, these calculations are just approximate, and I'm just a clown bot having some fun with numbers. So don't worry too much about what fraction is left in people's bones—strontium-90 is risky business anyway!
To determine the fraction of strontium-90 absorbed in 1962 that remained in people's bones in 1994, we can use the concept of half-life.
1. Start by calculating the number of half-lives that have passed from 1962 to 1994. To do this, divide the time between the two years (1994 - 1962 = 32 years) by the half-life of strontium-90 (27 years).
32 years / 27 years = 1.185 half-lives
2. Since we cannot have a fraction of a half-life, we need to round this value to the nearest whole number. In this case, we have 1 whole half-life that has passed.
3. Next, we need to calculate the fraction of strontium-90 that remains after 1 half-life. Each half-life reduces the amount of strontium-90 by half. Therefore, after 1 half-life:
Fraction remaining = 1/2 = 0.5
4. So, the fraction of strontium-90 absorbed in 1962 that remained in people's bones in 1994 is 0.5 or 1/2.
Therefore, approximately half of the strontium-90 absorbed in 1962 would still be present in people's bones in 1994.
To calculate the fraction of strontium-90 that remained in people's bones in 1994, we need to determine the number of half-lives that have passed from 1962 to 1994.
Step 1: Calculate the number of years that passed from 1962 to 1994.
1994 - 1962 = 32 years.
Step 2: Divide the number of years by the half-life of strontium-90.
32 years / 27 years (half-life of strontium-90) ≈ 1.185.
Step 3: Round the result to the nearest whole number to find how many half-lives have passed.
Since we can't have a fraction of a half-life, we round 1.185 to 1.
Step 4: Calculate the fraction of strontium-90 that remains.
To calculate the fraction that remains after one half-life, we divide 1 by 2, which gives us 0.5.
Therefore, approximately 0.5 or 50% of the strontium-90 absorbed in 1962 remained in people's bones in 1994.
1994-1962 = 32 years
(.5)^(1/27)=.974654
.5 because half life
.974654^32
Answer: 43.977
1994-1962 = 32 years
A = Ao*2^-t/27, so
A/Ao = 2^-32/27 = .4397 = 43.97%