How warm are radioactive metals? I read that radium is warm to the touch -- is that because of actual heat or is that because, for example, the radiation it emits creates the sensation of warmth? How high of a temperature can a radioactive element or isotope actually have?
 A: Yes radioactive materials are warmer than they would otherwise be. There are two reasons for this.
One is that the decayed atom will have picked up some kinetic energy in recoil and that is heat.
Another is that some of the radiation does not make it outside but hits another atom and transfers its energy to it as more heat. That includes any low-energy photons emitted by the decayed nucleus as it stabilises.
But how hot it gets depends on a variety of factors, such as the half-life, the total energy released in each decay, the concentration or richness of radioactive atoms in the material, the size vs surface area of the lump (the bigger it is, the proportionately less area it has to lose excess heat), and any cooling or insulating effects in its immediate environment.
At one end of the scale, such as a small piece of uranium ore, the heat is not enough to be measurable above background noise. At the other extreme you get a meltdown.
Natural radium is almost entirely radium 226. Its refined form appears to represent a borderline case. The following calculation is off-the-cuff and ignores any impurities, radioactive in themselves or otherwise, somebody please correct any mistakes! Radium 226 has a half-life of 1,600 years. One mole (gramme molecule) weighs 226 g and contains 6 X 1023 atoms. There are 5 x 1010 seconds in 1,600 years, so in the mole's first second of existence over 1013 atoms will decay. Its decay energy is 4.9 MeV, yielding say 4.9 x 10^23 eV or around 10^4 joules, enough to raise the temperature of 226 g of water by 10 degrees or so. The molecular weight of water is 20, so the temperature of the radium will increase by 10 x 20/226 or around 1 deg. That assumes no heat outflow from the radium; its actual temperature rise after an hour will be significantly lower, say 0.5 deg. Note that this is a rise above ambient, it is not an absolute value. Given a human hand several degrees warmer, and you may find that material properties like thermal conductivity may distort your subjective sense of warmth to the touch.
A: The interesting number for application in radioisotope thermoelectric generators is the power by weight. It is not very high for radium, as the half-life is 1600 years. The Pioneers use generators containing 13 kg of $^{238}$Pu with a halflife of 88 years. That has a power density of 0.54 W/g.
The linked wikipedia article says: "A half-gram sample of $^{210}$Po reaches temperatures of over 500 °C." (source at Argonne Laboratory).
A: Subcritical chunks of enriched uranium and plutonium are naturally warm to the touch, because of the thermal energy released as they spontaneously fission. Plutonium has a higher spontaneous fission rate and this effect is stronger for Pu.
If you place two such subcritical chunks near one another and slide them together gradually, at some point the neutrons released by one will induce extra fissions in the other, and the resulting energy release will make their facing sides hot enough to glow red.
Such (incredibly unsafe!) demonstrations and experiments were done at research laboratories like Los Alamos during the Manhattan Project. Two people died at Los Alamos due to radiation exposure when they slipped up while moving the chunks around. Don't do this at home!
