Does a smaller half-life mean that the rate of energy/radiation release is faster?

Question

I had a discussion with someone about using radioactive elements as sources of energy on board long interplanetary voyages. Actually we were talking about going to the moon, and what our source of energy would be. He said that the element that is used should have a long half-life, to have enough of it for the duration of the flight. I said that it would be better to have a short half-life, because the flight is a few tens of hours and since a long one would mean that on average it takes a long time for it to supply significant energy.

I want to ask you:

----Assumption to be taken: half-life is not probabilistic.----

Does a smaller half-life mean that the rate of energy/radiation release is faster?

The definition of half-life is the amount of time it takes for half an amount(in terms of mass) of a radioactive substance to disintegrate. Since this mass is lost by radiation(energy), does that mean that an inverse proportionality between half-life and rate of energy release exists?

My questions are:

If one has (x) mass of radioactive element (1) which has a half-life (a)

and (x) mass of radioactive element (2) which has a half-life (a/2).

1. Will element (2) release energy faster than element (1)?
2. If the question 1 is true, then does element (2) release energy twice as fast as element (1)?

Answer 1

The half life is not a guarantee of faster rate of energy release: just faster rate of disintegration. You need to multiply that by the energy released per disintegration to get the energy release per second.

All other things being equal (same atomic mass, same energy released), you need to bring less material (mass) along if you try to generate a certain amount of energy, if that material has a shorter half life.

The simple way to see that: if the total energy needed is released by 3000 atoms disintegrating, and the journey takes one half life, then I need to bring 6000 atoms along (half disintegrate). But if the half life is twice as short, I only need to bring 4000 atoms: after half the flight 2000 disintegrated, and another 1000 in the second half of the flight.

That demonstrates another problem: if you need constant power from your source, you need a longer half life...

In other words - it depends.