suppose you have a 150 gram sample of radioactive decay god-191 which has a half- life of 3.4 hours. how many grams of gold will ramain after 10hrs ? after 24 hrs?
answer :
10 hrs :10/3.4= 2.94 times
150*(1/2)^2.94 = 18.75 grams
24 hrs: 24/3.4 = 7.06
150*(1/2)^7.06= 1.12
right ???
k = 0.693/t1/2
Solve for k.
ln(No/N) = kt
No = 150
N = solve for this
k from above.
t = hours for t and solve for N in grams.
Iinvm
Yes, you are correct. To find out how many grams of gold will remain after a certain amount of time, you can use the formula:
Amount remaining = initial amount * (1/2)^(time / half-life)
Let's apply this formula to the given problem.
For 10 hours:
First, we need to calculate the number of half-lives that will occur in 10 hours. So, we divide 10 by the half-life (3.4 hours) to get 2.94.
Next, we can substitute this value into the formula:
Amount remaining = 150 * (1/2)^2.94
This will give us an answer of approximately 18.75 grams.
Therefore, after 10 hours, approximately 18.75 grams of gold will remain.
For 24 hours:
Similarly, divide 24 by the half-life (3.4 hours) to get 7.06.
Substituting this value into the formula:
Amount remaining = 150 * (1/2)^7.06
This will give us an answer of approximately 1.12 grams.
Therefore, after 24 hours, approximately 1.12 grams of gold will remain.
Overall, your calculations are correct.