If Pu239 emits alpha particles of energy 5.4Mev calculate the decay probability?

Answer 1

It is possible to relate a decay constant of some α emitting nucleus to an energy of α particle in the framework of the Gamow theory (see Related links) that is based on the quantum mechanics description of the tunneling through the potential barriers.

Previous view (by Quirkyquantummechanic)The fact that 239Pu decays by alpha particle emission (with the α particle coming away at 5.245 Mev) has nothing to do with this isotope of plutonium's decay probability. The decay probability of 239Pu (or anything else) can be expressed as a distribution function. That's math speak. What that means is that any nuclear decay event has "odds" that it may happen. Let's look at that a bit.

All unstable radionuclides will eventually decay. But when? Well, they all have some, um, "quirks" about them. Some take a long time to eventually fall apart, but some don't take that long. All we can do is "average out" the decay of a given material. Got that idea? It's important. And one of the ways we talk about the decay probability is in terms of something called the half life of a material. In the case of 239Pu, for example, the half life is 2.41 x 104 years. That's 24,100 years. What that means is that if we have a kilogram of the stuff, in 24,100 years, only half of the plutonium we started with will be left. Make sense? Mmhmm. But check this out. If we have two atoms of the stuff, does that mean that in 24,100 years only one will be here? No, it does not. They could both decay in the next week or the next month. Or the next century. Half life is a "probability thing" with unstable materials. And it is calculated across a "curve" of probability (that distribution function we mentioned) based on measurements of a quantity of the material being considered. It's that simple.

As an aside, but on a related note, if you guessed that the artificial elements (we call them synthetic, because they must be synthesized or made) that we know of by only a few atoms don't have very accurate measurements of their half lives, you'd be absolutely right. It's really difficult to (with accuracy) "guestimate" the half life of something, of some element, that is known from only a dozen atoms of the material....

Answer 2

The decay probability of a radioactive isotope is typically described by the decay constant, which is denoted by λ. The decay constant can be calculated using the formula λ = ln(2) / half-life. Once λ is known, the decay probability over a certain period of time can be calculated using the formula P = 1 - e^(-λt), where t is the time interval.