Alpha Decay Q-Value Calculator
Compute the alpha decay Q-value and the kinetic energy split between the alpha particle and the recoiling daughter nucleus.
💥 What is the Alpha Decay Q-Value Calculator?
This alpha decay Q-value calculator computes the total kinetic energy released when a nucleus emits an alpha particle, from the atomic masses of the parent, daughter, and alpha particle (helium-4), and splits that energy between the alpha particle and the recoiling daughter nucleus.
Alpha decay is common among heavy nuclei (uranium, thorium, radium, polonium, and their decay chains), where ejecting a tightly bound helium-4 nucleus is energetically favorable compared to the alternative decay modes. The released energy Q is shared between the alpha particle and the daughter nucleus according to momentum conservation, and because the alpha particle is so much lighter than the daughter, it carries away the vast majority of that energy.
A common point of confusion is treating the Q-value itself as "the alpha particle's energy." In reality, a small but measurable fraction of Q always goes into the daughter nucleus's recoil, this recoil energy is what allows techniques like recoil-implantation to isolate freshly-created daughter isotopes in nuclear physics experiments.
This calculator is useful for nuclear and particle physics students checking whether alpha decay is energetically allowed for a given isotope, and for computing the expected alpha particle energy to compare against measured decay spectra.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 - Uranium-238 alpha decay
Example 2 - Polonium-210 alpha decay
Example 3 - Radium-226 alpha decay
❓ Frequently Asked Questions
🔗 Related Calculators
What is the Q-value of an alpha decay?
The Q-value is the total kinetic energy released when a nucleus emits an alpha particle (a helium-4 nucleus). It is shared between the alpha particle and the recoiling daughter nucleus according to momentum conservation.
What is the formula for alpha decay Q-value?
Q_α = [M(parent) − M(daughter) − M_α] × 931.494 MeV/u, where all three masses are atomic masses in atomic mass units (u), and M_α≈4.0026032 u is the atomic mass of helium-4.
How is the released energy split between the alpha particle and the daughter nucleus?
By momentum conservation in the parent's rest frame, T_α = Q × M(daughter)/[M(daughter)+M_α] and T(daughter) = Q × M_α/[M(daughter)+M_α]. Since the alpha particle is much lighter than the daughter nucleus, it carries away most of Q.
Why does the alpha particle get most of the kinetic energy?
Momentum conservation requires the alpha particle and daughter nucleus to have equal and opposite momentum. Since kinetic energy at fixed momentum is inversely proportional to mass (T=p²/2m), the much lighter alpha particle ends up with far more kinetic energy than the heavy recoiling daughter nucleus.
What is a real example of alpha decay?
Uranium-238 decays to thorium-234 by alpha emission with Q≈4.270 MeV, of which the alpha particle carries about 4.198 MeV and the thorium-234 nucleus recoils with about 0.072 MeV, using atomic masses M(²³⁸U)=238.0507882 u and M(²³⁴Th)=234.0436012 u.
Why do heavier nuclei tend to be alpha emitters?
Alpha decay is energetically favorable primarily for heavy nuclei because the alpha particle (helium-4) is an unusually tightly bound configuration of 2 protons and 2 neutrons, making it energetically cheaper to eject than to lose 4 nucleons individually, especially once a nucleus is large enough that the Coulomb repulsion between protons outweighs the nuclear binding energy gained by staying together.
Can this calculator predict the alpha decay half-life?
No, the Q-value only tells you whether alpha decay is energetically allowed and how much energy is released, not how fast it happens. Half-life is governed separately by quantum tunneling through the Coulomb barrier (the Geiger-Nuttall law), which depends very sensitively on Q but requires a separate calculation.
What units does this calculator use for the masses?
Atomic mass units (u), where 1 u = 931.494 MeV/c², the standard unit used in published atomic mass tables (such as the AME evaluation) for the parent, daughter, and alpha particle (helium-4).
Does this formula work if I enter a different alpha particle mass?
The alpha particle mass field defaults to the helium-4 atomic mass (4.0026032 u) and should normally be left at that value, since true alpha decay always emits a helium-4 nucleus; the field is editable mainly so you can verify how sensitive the Q-value is to small changes in the input masses.
Is a negative Q-value ever observed in nature?
No, a negative Q-value means the decay is energetically forbidden and simply does not happen. Only isotopes with a positive alpha decay Q-value are observed to be alpha emitters; this calculator's allowed/forbidden check reflects that same physical requirement.