The half life of tritium is 12.3 yr. If 62.2mg of tritium is released from a nuclear power plant during the course of an accident, what mass of this nuclide will remain after 105 yr?
62.2 mg (1/2)^(105/12.3)
To determine the mass of tritium that will remain after 105 years, we can use the formula for exponential decay:
N(t) = N₀ * (1/2)^(t / half-life),
where:
N(t) is the remaining amount of tritium after time t,
N₀ is the initial amount of tritium,
t is the time passed, and
half-life is the time it takes for half of the substance to decay.
First, we need to calculate the initial amount of tritium. We know that 62.2 mg of tritium was released, representing the initial amount (N₀).
Also, the half-life of tritium is given as 12.3 years.
So, plugging these values into the formula, we have:
N(t) = 62.2 mg * (1/2)^(105 years / 12.3 years).
Now we can calculate:
N(t) = 62.2 mg * (1/2)^(8.54).
Finally, evaluating the expression:
N(t) ≈ 62.2 mg * 0.168.
N(t) ≈ 10.43 mg.
Therefore, approximately 10.43 mg of tritium will remain after 105 years.