An element has a half-life of 30 years. If 1.0 mg of this element decays over a period of 90 years, how many mg of this element would remain?
Begin amount is 1.0
elapsed time is 90y half life 30 years
n=9/30 n=3
90/2^2
90/8 = 11.25mg
thinking it's wrong not sure what I missed.
A 2.5 gram sample of a radioactive element was formed in a 1960 explosion of an atomic bomb at Johnson Island in the Pacific Test Site. The half-life of the radioactive element is 28 years. How much of this element will remain after 112 years?
I tried it this way 112/28= 4 half lives then 2.5/3 1.25
1.25/2=0.625
06.25/2= 0.3125
0.3125/2=0.15625 gram
which is the correct way to do these problems. Am I doing that the correct way
90 years is 3 half-lives. That means that 1/8 of the original amount remains. So, the 1 mg that has decayed represents 7/8 of the original amount. So, starting out at 8/7 g, 1/7 g = 14.27mg remains.
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after 4 half-lives, 1/16 of the original amount remains.
2.5/16 = 0.15625g
you are correct
Yes, you are on the right track, but there are some mistakes in your calculations.
For the first question, you have correctly determined that the number of half-lives elapsed is n = elapsed time / half-life = 90 years / 30 years = 3 half-lives.
To calculate the remaining amount of the element, you need to use the formula:
Remaining amount = initial amount * (1/2)^(number of half-lives)
In this case, the initial amount is 1.0 mg and the number of half-lives is 3. So the calculation would be:
Remaining amount = 1.0 mg * (1/2)^3 = 1.0 mg * (1/8) = 0.125 mg
Therefore, after 90 years, 0.125 mg of the element would remain.
For the second question, you have correctly determined that the number of half-lives elapsed is n = elapsed time / half-life = 112 years / 28 years = 4 half-lives.
To calculate the remaining amount of the element, you can use the same formula:
Remaining amount = initial amount * (1/2)^(number of half-lives)
In this case, the initial amount is 2.5 grams and the number of half-lives is 4. So the calculation would be:
Remaining amount = 2.5 g * (1/2)^4 = 2.5 g * (1/16) = 0.15625 g
Therefore, after 112 years, 0.15625 grams of the element would remain.
So, both of your calculations are correct, but the decimal point placement needs to be adjusted in the answer for the first question.
For the first problem, the correct way to calculate the remaining amount of the element after 90 years is as follows:
1. Determine the number of half-lives that have passed: 90 years / 30 years = 3 half-lives.
2. Apply the half-life equation: Remaining amount = Initial amount / (2^(number of half-lives)).
3. Calculate the remaining amount: Remaining amount = 1.0 mg / (2^3) = 1.0 mg / 8 = 0.125 mg.
Therefore, after 90 years, 0.125 mg of the element would remain.
For the second problem, your approach is correct:
1. Determine the number of half-lives that have passed: 112 years / 28 years = 4 half-lives.
2. Apply the half-life equation: Remaining amount = Initial amount / (2^(number of half-lives)).
3. Calculate the remaining amount: Remaining amount = 2.5 g / (2^4) = 2.5 g / 16 = 0.15625 g.
Therefore, after 112 years, 0.15625 grams of the element would remain.