the half life of H-3 is 12.26 years. What percentage is left after 0.100 centuries?

Answer 1

You need to use the equation for radioactive decay to handle this. We write this in general form as:

N(t) = N0 exp(-kt) where N(t) is the number of nuclei remaining at time t, N0 is the original number of nuclei, k is a constant related (but not equal to the half life) and t is the time elapsed.

You can show that the constant k=ln 2/halflife, where ln is the natural logarithm, so for this case, k = ln2/12.26=0.69/12.26 = 0.0563.

Since we are using half life in years, we should use time in years, and 0.1 centuries is then ten years.

If we substitute these values into our equation, we get:

N(10)=N0 exp(-0.0563x10) = N0 exp(-0.563)=0.57N0, or in other words, we have 57% of the remaining nuclei of tritium (H-3) after 10 yrs.

If you step back and look at this, this answer should make sense. In 12.26 years you expect to be down to one half of the original number of nuclei, but in ten years, you have not quite elapsed through one full half life, so expect slightly more than half the nuclei to remain.

Answer 2

1-e^10/12.26