Question

Tritium (H-3) has a half-life of 12.3 years. How old is a bottle of olive oil if the tritium content is 25% that of a new sample of olive oil? Show all calculations leading to a solution.

Answer 1

24.6 years = 2 half-lifes

Answer 2

it lost 50 percent of the normal tritium.
In the second half-life it lost the 50percent of the 50percent so only the 25 percent of the original..
t1/2 = 0.693 k with this formula you can calculate the k of the reaction.
then with the k you can calculate on how many years In(A)f= -kt+In(A)0
Where you have to calculate T thinking that (A)0=100 and (A)=25

Answer 3

Because half-life means final amount becomes 50% of original, therefore, after another half-life time, the final amount becomes 25% of original. Well if you look at the problem, all you have to do is multiply the the half-life 12.3 years by 2, which is 24.6 years. But if you want the method using formula, I also wrote it here.

Decay formula (I won't show the derivation of this):
A = Ao * e^(-kt)
where
A = final amount after some time, t
Ao = initial amount
k = constant
t = time

First, we get the constant, k, using the info about its half-life. Note that half-life means that the final amount is equal to 1/2 of the original amount, or A/Ao = 0.5. Substituting,
0.5 = e^(-kt)
0.5 = e^(-k * 12.3)
Get the natural log (ln) of both sides:
ln 0.5 = ln e^(-k * 12.3)
-0.693 = -12.3 * k
k = 0.693/12.3
k = 0.05635

Now we can solve for t in the problem using the value of k we obtained.
A = Ao * e^(-kt)
It says that the final amount is 255 of the original thus,
0.25 = e^(-kt)
0.25 = e^(-0.05635 * t)
Get the ln:
ln 0.25 = -0.05635 * t
-1.386 = -0.05635 * t
t = 1.386 / 0.05635
t = 24.6 years

Hope this helps~ `u` (Though I see you've answered it already ^^;)

Answer 4

yes but Thank you jai :)