I'm wondering if the temperature could affect the half-life in an element. For example, Carbon 14 has a half-life of 5,730 years. Is this always true or only true for standard conditions of temperature and pressure? Also, if that does affect, how does it affect?
Asked
Active
Viewed 5,712 times
2 Answers
12
Temperature affects the half-life via time dilation. If the half-life of a nucleus as observed in its rest frame is $\tau(0)$, then in some other frame in which it moves at a speed of $v$, it will be:
$$\tau(v) =\frac{\tau(0)}{\sqrt{1-\dfrac{v^2}{c^2}}}$$
Because the typical thermal speeds of atoms at room temperature are much smaller than the speed of light, we may expand the above expression to leading order. This yields:
$$\tau(v) =\tau(0)\left[1 + \frac{v^2}{2c^2}+\cdots \right]$$
The average of the square of the speed over the velocity distribution of atoms at temperature $T$ follows from the equipartition theorem. The average energy in each degree of freedom of a gas is $\frac{1}{2} k T$, this means that the average of the kinetic energy is $\frac{3}{2} k T$, it then follows that:
$$\left\langle v^2\right\rangle = \frac{3 k T}{m}$$
Therefore, the leading temperature dependence of the half-life is given by:
$$\tau =\tau(0)\left[1 + \frac{3 k T}{2mc^2}+\cdots \right]$$
For carbon-14 at $25 ^{\circ}$ C the term $ \dfrac{3 k T}{2mc^2}$ is $2.95\times 10^{-12}$. Since the experimental error in the half life is about 0.7% this effect is too small to be observed.
Count Iblis
- 10,396
- 1
- 25
- 49
2
Pierre Curie checked this out in 1913 by cooling radium in liquid hydrogen and found that the half life was the same as room temperature...radioactive decay is independent of temperature. I am seeing other answers that provide more detail, but this I would say is the simple answer.
brielmannh
- 81