← Nuclear Physics

# Alpha Decay

Sunday, April 3, 2022

## The Alpha Decay Process

In an alpha decay process, an unstable nucleus decays into a lighter nucleus and an alpha particle (a nucleus of $^4\text{He}$):

$^A_ZX_N\rightarrow~^{A-4}_{Z-2}X'_{N-2}+~^4_2\text{He}_2$

where $X$ and $X'$ represent different nuclei.

The excess energy released from the process (since the resulting nucleus is more tightly bound than the initial one) is found using the atomic masses of the particles:

$Q=\left[m\left(X\right)-m\left(X'\right)-m\left(^4\text{He}\right)\right]c^2$

The energy $Q$ is used as kinetic energy by the particles:

$Q=K_{X'}+K_\alpha$

Additionally, due to conservation of linear momentum, we know

$p_\alpha=p_{X'}$

Using non-relativistic mechanics, we can find that

$K_\alpha\approxeq\frac{A-4}{A}~Q$

## Some Alpha Decay Energies and Half-Lives

Below are some decay energies and their associated half-lives for some isotopes:

Isotope $K_\alpha~\left(\text{MeV}\right)$ $t_{1/2}$ $\lambda~\left(\text{s}^{-1}\right)$
$^{232}\text{Th}$ $4.01$ $1.4\times 10^{10}~\text{y}$ $1.6\times 10^{-18}$
$^{238}\text{U}$ $4.20$ $4.5\times 10^9~\text{y}$ $4.9\times 10^{-18}$
$^{230}\text{Th}$ $4.69$ $7.5\times 10^4~\text{y}$ $2.9\times 10^{-13}$
$^{241}\text{Am}$ $5.54$ $433~\text{y}$ $5.1\times 10^{-11}$
$^{230}\text{U}$ $5.89$ $20.8~\text{d}$ $3.9\times 10^{-7}$
$^{210}\text{Rn}$ $6.04$ $2.4~\text{h}$ $8.0\times 10^{-5}$
$^{220}\text{Rn}$ $6.29$ $56~\text{s}$ $1.2\times 10^{-2}$
$^{222}\text{Ac}$ $7.01$ $5~\text{s}$ $0.14$
$^{215}\text{Po}$ $7.39$ $1.8~\text{ms}$ $3.9\times 10^{2}$
$^{218}\text{Th}$ $9.67$ $0.12~\mu\text{s}$ $6.3\times 10^{6}$