suppose you have 100grams of radioactive plutonium-239 with a half-life of 24,000 years. how many grams of plutonium-239 will remain after:
A)12,000 years
B)24,000 years
C)96,000 years
how do i do this??????
Here is how you do the first one.
k = 0.693/t1/2
Substitute 24,000 for t1/2 in the above equation and calculate k. Then substitute k into the following equation.
ln(No/N) = kt
No = 100 grams = what you start with.
N = what you end up with and this is the unknown.
k from above.
Solve for N.
Use the same procedure for parts B and C. The answer for N will be in grams since No is in grams.
Post your work if you get stuck.
Well, there would be 50 grams left after 24,000 years. And if you divide both by two, you get __grams(try that yourself!) after 12,000 years. And, if you multiply that (1st problem I did) by 2, you get __grams after 96,000 years. Notice that everything is a multiple of 2.
Hope that helps!
Let me know what answers you got for the A and C (I gave you the answer for B), and I'll tell you if you're right! :)
Food4thought needs to rethink the answers s/he gave. The answer for 24,000 years (part B) is correct. I don't understand the answer for part A (12,000 years) and the answer for part C gives the same amount (2 x 50 = 100 g) we started with so it CAN'T be correct. Not much truth and little reality in these answers. (Sorry, I couldn't resist.)
t in the second equation is, of course, the time which for part a is 12,000, part b is 24,000, etc.
To determine the amount of radioactive plutonium-239 that will remain after a certain time period, you can use the concept of half-life. The half-life is the time it takes for half of the radioactive substance to decay.
In this case, the half-life of plutonium-239 is 24,000 years. So, after every 24,000 years, half of the initial amount will decay.
Let's calculate the remaining amount after each time period:
A) After 12,000 years:
Since the half-life is 24,000 years and 12,000 years is exactly half of that, we can conclude that half of the initial amount has decayed. Therefore, the remaining amount after 12,000 years would be 50 grams (half of 100 grams).
B) After 24,000 years:
Since the half-life is 24,000 years, the entire initial amount will decay after 24,000 years. Hence, there will be 0 grams of plutonium-239 remaining.
C) After 96,000 years:
To calculate the remaining amount after 96,000 years, we need to find out how many times the half-life of 24,000 years fits into this time period. Here, 96,000 years divided by 24,000 years equals 4. So, after four half-lives, we are left with one-sixteenth (1/2^4) of the initial amount. Thus, the remaining amount after 96,000 years would be 6.25 grams (100 grams divided by 2^4).
So, the answers are:
A) 50 grams
B) 0 grams
C) 6.25 grams