Beta Decay Q-Value Calculator
Compute the Q-value for beta-minus decay, beta-plus decay, or electron capture from the parent and daughter atomic masses.
☢️ What is the Beta Decay Q-Value Calculator?
This beta decay Q-value calculator computes the total kinetic energy released (Q) in β⁻ decay, β⁺ decay, or electron capture, from the atomic masses of the parent and daughter isotopes.
Each beta decay mode has a slightly different formula because of how atomic electrons are created, destroyed, or captured in the process. β⁻ decay converts a neutron into a proton, ejecting an electron and an antineutrino. β⁺ decay converts a proton into a neutron, ejecting a positron and a neutrino. Electron capture achieves the same nuclear transformation as β⁺ decay by absorbing an atomic electron instead of creating a positron, which is why it has a less strict energy requirement.
A common point of confusion is why these formulas use atomic masses (which include all the bound electrons) rather than bare nuclear masses. Using atomic masses is a deliberate convenience: the electron masses cancel correctly in the β⁻ and electron-capture formulas without any extra terms, and only β⁺ decay needs an explicit −2mₑ correction.
This calculator is useful for nuclear and particle physics students checking which decay modes are energetically allowed for a given isotope, and for verifying textbook Q-value calculations against published atomic mass tables.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 - Carbon-14 β⁻ decay (radiocarbon dating)
Example 2 - Sodium-22 β⁺ decay (PET calibration source)
Example 3 - Potassium-40 electron capture (K-Ar dating)
❓ Frequently Asked Questions
🔗 Related Calculators
What is the Q-value of a beta decay?
The Q-value is the total kinetic energy released in a beta decay, shared among the decay products (the daughter nucleus, the beta particle, and the neutrino). A positive Q-value means the decay is energetically allowed; a negative or zero Q-value means it is forbidden.
What is the formula for β⁻ decay Q-value?
Q_β⁻ = [M(parent) − M(daughter)] × 931.494 MeV/u, using the atomic masses of the parent and daughter in atomic mass units (u). The extra atomic electron in the daughter atom exactly accounts for the electron created in the decay.
What is the formula for β⁺ decay Q-value?
Q_β⁺ = [M(parent) − M(daughter) − 2mₑ] × 931.494 MeV/u, where mₑ≈0.00054858 u is the electron mass. The extra 2mₑ accounts for creating a positron and having one fewer bound electron in the daughter atom compared to β⁻ decay.
What is the formula for electron capture Q-value?
Q_EC = [M(parent) − M(daughter)] × 931.494 MeV/u, the same mass-difference formula as β⁻ decay, since a captured atomic electron simply disappears into the nucleus rather than being created.
Why does β⁺ decay require 2 more electron masses than β⁻ decay?
β⁻ decay converts a neutron to a proton and creates an electron, which becomes the daughter atom's extra bound electron (net electron count is unchanged in the formula). β⁺ decay converts a proton to a neutron and creates a positron while losing a bound electron from the daughter atom, a net change of 2 electron masses compared to β⁻.
What is a real example of β⁻ decay?
Carbon-14 decays to nitrogen-14 by β⁻ decay with Q≈0.156 MeV, the small but positive Q-value behind carbon dating, using atomic masses M(¹⁴C)=14.0032420 u and M(¹⁴N)=14.0030740 u.
What is a real example of β⁺ decay?
Sodium-22 decays to neon-22 by β⁺ decay with Q≈1.820 MeV, using atomic masses M(²²Na)=21.9944364 u and M(²²Ne)=21.9913851 u, matching the measured Q-value used in PET imaging calibration sources.
What is a real example of electron capture?
Potassium-40 decays to argon-40 by electron capture with Q≈1.505 MeV, using atomic masses M(⁴⁰K)=39.9639982 u and M(⁴⁰Ar)=39.9623831 u, part of the potassium-argon dating method used in geochronology.
Can an isotope decay by electron capture but not by β⁺ decay?
Yes. Electron capture only needs Q_EC=[M(parent)−M(daughter)]×931.494 MeV/u to be positive, while β⁺ decay needs the stricter Q_β⁺=[M(parent)−M(daughter)−2mₑ]×931.494 MeV/u to be positive, an extra 1.022 MeV threshold. Isotopes with a small positive mass difference can satisfy the first condition but not the second.
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 both parent and daughter isotopes.