POLONIUM 212
ABOUT POLONIUM 212
The incredible range of alpha decay half-lives can be modeled with quantum mechanical tunneling. The barrier faced by an alpha particle in POLONIUM-212, which emits an 8.78 MeV alpha particle with a half-life of 0.3 microseconds. The following characteristics of the nuclear environment can be calculated from a basic model of the nucleus: Separation of centers of alpha and nucleus at edge of barrier *9.1 fm* Height of barrier *26.4 MeV* Radius at which barrier drops to alpha energy *26.9 fm* Width of barrier seen by alpha *17.9 fm* Alpha's frequency of hitting the barrier *1.1 x 10^21/s* Details of calculation Different isotopes The shape of the barrier must obviously be taken into account since it drops rapidly. But it is instructive to calculate the half-life for a rectangular barrier of that height and width. Using the barrier penetration calculation gives a half-life of 1.5 x 10^7 seconds, about 13 orders of magnitude longer than the observed half-life. This gives some insight into the large range of alpha half-lives; the tunneling probability depends very strongly on the nature of the barrier. The probability depends exponentially on the height and width, and in this case the height is dropping like 1/r with distance from the nucleus.
