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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 4He^4\text{He}):

ZAXN→ Z−2A−4XN−2′+ 24He2^A_ZX_N\rightarrow~^{A-4}_{Z-2}X'_{N-2}+~^4_2\text{He}_2

where XX and X′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=[m(X)−m(X′)−m(4He)]c2Q=\left[m\left(X\right)-m\left(X'\right)-m\left(^4\text{He}\right)\right]c^2

The energy QQ is used as kinetic energy by the particles:

Q=KX′+KαQ=K_{X'}+K_\alpha

Additionally, due to conservation of linear momentum, we know

pα=pX′p_\alpha=p_{X'}

Using non-relativistic mechanics, we can find that

Kα≊A−4A QK_\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 Kα (MeV)K_\alpha~\left(\text{MeV}\right) t1/2t_{1/2} λ (s−1)\lambda~\left(\text{s}^{-1}\right)
232Th^{232}\text{Th} 4.014.01 1.4×1010 y1.4\times 10^{10}~\text{y} 1.6×10−181.6\times 10^{-18}
238U^{238}\text{U} 4.204.20 4.5×109 y4.5\times 10^9~\text{y} 4.9×10−184.9\times 10^{-18}
230Th^{230}\text{Th} 4.694.69 7.5×104 y7.5\times 10^4~\text{y} 2.9×10−132.9\times 10^{-13}
241Am^{241}\text{Am} 5.545.54 433 y433~\text{y} 5.1×10−115.1\times 10^{-11}
230U^{230}\text{U} 5.895.89 20.8 d20.8~\text{d} 3.9×10−73.9\times 10^{-7}
210Rn^{210}\text{Rn} 6.046.04 2.4 h2.4~\text{h} 8.0×10−58.0\times 10^{-5}
220Rn^{220}\text{Rn} 6.296.29 56 s56~\text{s} 1.2×10−21.2\times 10^{-2}
222Ac^{222}\text{Ac} 7.017.01 5 s5~\text{s} 0.140.14
215Po^{215}\text{Po} 7.397.39 1.8 ms1.8~\text{ms} 3.9×1023.9\times 10^{2}
218Th^{218}\text{Th} 9.679.67 0.12 μs0.12~\mu\text{s} 6.3×1066.3\times 10^{6}