half life of tritium is 12.5 years. how much will remain after 100 years if you started wit 256 grams?
First determine k.
k = 0.593/t1/2, then substitute the value of k into the equation below.
ln(256/N) = k(100)
Solve for N in grams.
Thanks so much!
I made two typos. k = 0.693/t1/2
To determine how much tritium will remain after 100 years, we can use the formula for exponential decay:
N = N₀ * (1/2)^(t / T)
Where:
- N is the final amount of the substance
- N₀ is the initial amount of the substance
- t is the elapsed time
- T is the half-life of the substance
In this case, the initial amount N₀ is 256 grams, the half-life T is 12.5 years, and the elapsed time t is 100 years.
Using the formula, we can calculate the final amount of tritium remaining after 100 years:
N = 256 * (1/2)^(100 / 12.5)
Now we can solve the equation.
N = 256 * (1/2)^(8)
To calculate (1/2)^(8), we raise 1/2 to the power of 8.
(1/2)^8 = 1/256
Now we substitute this into our equation:
N = 256 * (1/256)
N = 1 gram
Therefore, after 100 years, if you started with 256 grams of tritium, only 1 gram will remain.