# Energy as a function of half-life?

How much energy is released in the radioactive substance's decay of one cycle of its half life? I'd like the plot the energy released of a radioactive substance over time. What must I reference to determine this? The type of decay? The substance? Am I correct that the ionizing radiation that results from radioactive decay weakens in proportion to the square of the distance?

The energy released is the difference between the energy of the reactants and the energy of the products: $$\Delta E=E_0-E_f$$ In reality, you have to account for the kinetic energy of the products. See this Wikipedia article for more information.

The energy released over one cycle of half-life would be the decay energy times the number of decays that occurred, which, over one half-life, would be half the atoms in the initial sample.

The flux of the energy leaving by radiation across a surface should be constant to conserve energy, so the intensity of this radiation would indeed have an inverse-square characteristic.3n

Am I correct that the ionizing radiation that results from radioactive decay weakens in proportion to the square of the distance?

This is true as long as absorption in the intervening medium (e.g. air) is insignificant. So gamma ray intensity will decrease as the square of the distance. But the intensity of alpha and beta radiation will fall off more rapidly (unless you are in a vacuum).

How much energy is released in the radioactive substance's decay of one cycle of its half life?

The energy released in one decay (which depends on the isotope and the particular decay mode) times the number of decays, which in this case, equals half the number of isotopes you start out with.

I'd like the plot the energy released of a radioactive substance over time.

That will simply be the usual exponential decay, times some constant average energy released per decay.

Am I correct that the ionizing radiation that results from radioactive decay weakens in proportion to the square of the distance?

In general yes, but that may depend on your actual setting and whether you're solving back-of-the-envelope physics problems or addressing actual radiation safety issues.