## alpha decay

different decay cause by deferent mechanism, we first start on alpha decay.

i assume we know what is alpha decay, which is a process that bring excited nucleus to lower energy state by emitting an alpha particle.

The force govern this process is the strong force, due to the force is so strong, the interaction time is very short, base on the uncertainty principle that large change in energy leads to short time interval. however, the observed alpha decay constant is about 1.3 × 1010 year, which is about the age of our universe. That’s why we still able to find it at the beginning of nuclear physics : discovery of radioactive matter.

The reason for such a long decay time is due to the Coulomb barrier of the nuclear potential. since the proton carry positive charge, thus. it creates a positive potential wall in the nucleus. that potential not only repulse proton from outside but also the proton from inside which try to get out. thus, the inside protons are bounded back and forth inside the nucleus. due to the momentum carried by the protons, it has frequency 6  × 1021 per sec.

Due to the Quantum tunneling effect, the probability of tunneling is 4 × 10-40. which is a very small chance. But , don’t forget there are  6  × 1021 trails per sec. Thus, the chance per sec is 2.4 × 10-18 . and the mean life time is inverse of the probability, thus it is approx 1.3 × 1010 year.

## decay

the decay idea and mathematic is simple. so, i just state it.

Number of particle (time) = Initial # of particle × Exp( – time / T )

or in formula

$N(t) = N(0) Exp \left( - \frac {t} {T} \right )$

where T is time constant, which has a meaning that how long we should wait before it decay. T also has another name, “mean-lifetime“, coz when you find out the mean of their life by usually statistical method, integrate the whole area of the graph of decay time and make it equal to initial # of particle × “mean lifetime”. that is what you got. ( $\int_0^\infty Exp( - \frac {t}{T}) dt= T$ )

some people like to write the equation is other way:

$N(t) = N(0) Exp \left( - R t \right )$

where R is the chance of decay in unit time. which is just the “invert” meaning of T.

we also have “Half-Life$t_\frac {1}{2}$, which is the time that only half of the particle left. by the equation, we have:

$t_\frac {1}{2} = ln(2) T$

thus, a longer T, the particle live longer, as what is the T mean!

But above mathematics only tell us the statistic result of the decay, not about the mechanism, or physics of what cause the decay happen. why there is decay? why particles come out from nucleus? how many kind of decay ?

the easiest question is, there are 3 decay happen in nature and a lot more different decay happened in lab. the reason for only 3 decay is that, only these 3 live long enough to let us know. the other, they decay fast and all of them are done.

and the reason for nucleus decay is same as the reason for atomic decay. excited nucleus is unstable (why?) they will emit energy to become stable again.

and the physics behind decay, we will come back to it later.