# Does hotter radioactive substance have longer half life?

Sorry to have a newbie question! But I want to ask, if it is possible to change the half life of radioactive substance by heating it, my hypothesis is:

1. When substance becomes hotter, the kinetic energy of atom is greater

2. The atoms collides more frequently, that means the atoms accelerate and decelerate more frequently

3. When atoms accelerates and decelerates, the acceleration time dilation cause the time elapse of the atoms become slower, so it has smaller chance to decay

4. As the chance of decay of each atom decreases, the half life of the radioactive substance becomes longer

Is the hypothesis true?

• You are conflating a number of concepts here. by 'Hot radio-isotopes' is usually simply meant 'short lived' ones.
– Gert
Commented Dec 31, 2015 at 3:05

## 2 Answers

The short answer is yes, the half life of a hot substance will be longer! But only very slightly. Though it's not because they're accelerating, but rather because they're moving faster.

Let's work out roughly how large the effect is. To make it as large as possible, let's take some very light particles so they move as fast as possible for a given kinetic energy. The lightest radioactive nucleus found in nature is tritium, an isotope of hydrogen consisting of a proton and two neutrons.

Molecules in a gas of tritium will have speeds roughly following the Maxwell-Boltzmann distribution, which we could use if we wanted to be really precise, but to get a ballpark figure we can estimate the speed of the molecules using just dimensional analysis. The only scales in the problem are the mass of the molecules $m$, and the temperature $T$, and we'll also need Boltzmann's constant to convert from units of temperature to energy. The only speed we can build from this is $$v \sim \sqrt{\frac{kT}{m}}$$ Putting in the mass of a tritium molecule (6 nucleon masses, because there are two atoms in each gas molecule), and room temperature, we get around 600 metres per second, or 2 millionths of the speed of light.

The time-dilation effect will change the half-life by a factor of $\gamma$, which is $$\gamma = \frac{1}{\sqrt{1-v^2/c^2}} \approx 1+\frac{v^2}{2c^2}$$ where the approximation uses the binomial theorem, and works for speeds much less then $c$. For our room-temperature tritium, this is roughly an extra factor of $2*10^{-12}$: a really tiny amount! The tritium half-life is 12 years, and the relativistic effect of room temperature adds about a millisecond to that. Needless to say, this would be a very hard effect to measure!

True? Yes, but the effect is negligible for normal tempratures. One situation that does illustrate your point is the decay of high energy muons that get created in the atmosphere by cosmic ray bombardment. Many more reach the ground than would be expected from their normal half life because their high speed lengthens their halflife.

• Note that the halflife doesn't really change -- the muon's clock is just running slower to an outside observer (due to its speed). If you rode along with the muon while watching it, your clock would slow down too, and its halflife would appear to be normal. Commented Mar 5, 2020 at 16:18