24Na Beta Decay Calculator: Sodium-24 to Magnesium-24

A 24Na beta-decay calculator works out the daughter nuclide and the energy released when sodium-24 undergoes beta-minus decay; enter the parent and daughter nuclear masses to calculate the Q-value in MeV. Sodium-24 decays to magnesium-24, emitting an electron and an electron antineutrino; this calculator is a mass-based calculation, not a prediction of decay timing or radiation dose.

Formula

For beta-minus decay written using neutral atomic masses, the energy release is Q = (M_parent − M_daughter)c². The calculator expresses the mass difference in unified atomic mass units (u), then multiplies by 931.49410242 MeV/u, the energy equivalent of one atomic mass unit.

• M_parent is the neutral atomic mass of sodium-24, in u.
• M_daughter is the neutral atomic mass of magnesium-24, in u.
• Q is the decay energy in MeV.
• Energy equivalent converts Q to kilojoules per mole of decays using 1 MeV per particle = 96.4853321233 kJ/mol.

For beta-minus decay, a neutron changes into a proton while producing an electron and an electron antineutrino: n → p + e⁻ + ν̄_e. At the nuclear level, the atomic number rises by one and the mass number stays the same. Using neutral atomic masses, the electron masses cancel appropriately in the mass-difference relation, so no extra electron-mass term is added to this formula. Do not mix atomic masses with bare nuclear masses: they require different bookkeeping.

Worked Example

Using the calculator’s default atomic masses, M_parent = 23.990963 u and M_daughter = 23.985042 u:

1. Find the mass difference: 23.990963 u − 23.985042 u = 0.005921 u.
2. Convert the mass difference to energy: Q = 0.005921 × 931.49410242 = 5.514? MeV. More precisely, Q ≈ 5.514? MeV; the displayed six-decimal value is determined directly by the entered masses and conversion constant.
3. Convert to the molar energy equivalent: Q × 96.4853321233 kJ/mol, with Q in MeV per decay.

Important: the default masses above are rounded representations, and arithmetic must use their stated values. Their difference is 0.005921 u, giving Q = 5.514? MeV. Consult a current evaluated nuclear-mass source for a precision result; rounded defaults are illustrative. The precise final digits should not be interpreted as a recommended nuclear-data value.

Assumptions

• The inputs are neutral atomic masses in u, not mass numbers or masses in kilograms.
• The listed energy is the total available decay energy (Q-value), not the kinetic energy of one emitted particle.
• The calculation treats the daughter state as the ground state; an excited daughter state reduces energy available to the emitted particles by its excitation energy.
• The energy-per-mole output means a mole of individual decays, not a mole of sodium-24 atoms at a particular time.

What Sodium-24 Beta Decay Means

Sodium-24, written ²⁴Na, has 11 protons and 13 neutrons. In beta-minus decay one neutron converts to a proton, producing magnesium-24, ²⁴Mg, with 12 protons and 12 neutrons. Conservation of electric charge and nucleon number is reflected in the equation:

²⁴Na → ²⁴Mg + e⁻ + ν̄_e

The electron is often called the beta particle. The antineutrino carries away part of the energy and momentum. The daughter nucleus may also be produced in an excited state; it can then release that excitation energy, commonly through gamma radiation. A simple mass-difference calculator does not model the detailed decay scheme or the energy spectrum of the emitted beta particles.

Sodium-24 is radioactive and has a half-life of about 15 hours. Half-life describes the statistical reduction in the number of undecayed nuclei in a large sample: after one half-life, about half remain; it does not mean that each individual atom decays on a schedule. The half-life is separate from Q-value, so it is not an input in this calculator.

How to Use the Result

Enter reliable atomic masses for the parent and daughter nuclides in u. The defaults are convenient rounded values for a worked illustration, not a substitute for evaluated nuclear data. The first result is Q in MeV, the total energy release per decay under the ground-state assumption. The second is the corresponding energy per mole of decays.

• Use the nuclide masses for the exact isotopes, not ordinary sodium or magnesium average atomic weights.
• Keep the mass convention consistent. If you use nuclear masses, account for electron masses and binding-energy conventions correctly rather than applying the atomic-mass formula unchanged.
• Use enough mass precision for the required energy precision. Subtracting similar masses can make rounding in the inputs significant.
• A positive Q means the decay is energetically allowed for the specified final state. It does not by itself give the decay probability or half-life.

Energy, Spectrum, and Half-Life

Q is a budget shared among the decay products, not a single fixed beta-particle energy. In beta decay, the electron and antineutrino share energy continuously, while recoil also takes a small amount. If the daughter is formed excited, subsequent gamma emission accounts for that nuclear excitation. Therefore, a beta spectrum’s endpoint is related to Q, but most beta particles do not necessarily carry all of Q.

To calculate how much sodium-24 remains after a time, use radioactive-decay mathematics instead: N(t) = N₀ × 2^−t/T_1/2, where N₀ is the initial number of nuclei, t is elapsed time, and T_1/2 is the half-life. That calculation requires an initial amount and elapsed time and answers a different question than the mass-to-energy calculator here.

Common Errors and Limits

A mass number such as 24 is a count of protons plus neutrons; it is not an atomic mass of exactly 24 u. Substituting mass numbers into the formula gives a zero difference for two nuclides with mass number 24 and therefore a meaningless Q-value. Use isotope-specific masses instead.

Another frequent error is to treat Q as the beta particle’s measured kinetic energy. The antineutrino and recoil share energy, and nuclear excited states change the available amount. Also, the energy-per-mole output is a unit conversion, not a statement that one laboratory sample will release that energy at once. Actual radioactive samples require appropriate radiation controls and are not suitable for casual handling. For any bench work involving radioactive material, follow your lab method, the safety data sheet (SDS) and your supervisor.

This calculator does not determine activity, dose, shielding, detector response, branching ratios, daughter-state energies, or a full beta spectrum. Those require additional nuclear and radiation data. For research-grade values, use an evaluated mass table and decay dataset, record the source and precision, and verify whether the mass refers to a ground or excited state.

Frequently Asked Questions

What does 24Na decay into?
It decays by beta-minus emission to magnesium-24. The process also emits an electron antineutrino, and the magnesium nucleus may be left excited.

Why does the atomic number change but the mass number stay 24?
A neutron becomes a proton, so the number of protons rises from 11 to 12. The total number of protons and neutrons remains 24.

Is the Q-value the energy of the beta particle?
No. Q is the total energy available from the mass difference. The beta electron, antineutrino, and nuclear recoil share it, with further energy accounting needed for an excited daughter state.

Can I use 24 and 24 as the masses?
No. Those are mass numbers, not isotope-specific atomic masses. Their difference is not accurate enough to calculate decay energy.

Does this calculator tell me how fast sodium-24 decays?
No. It calculates energy from masses. Decay rate is described by half-life and requires a separate calculation.

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in mp | Parent atomic mass (sodium-24) | u | 23.990963 | 0
in md | Daughter atomic mass (magnesium-24) | u | 23.985042 | 0
out q | Beta-minus decay energy Q | MeV | (mp - md) * 931.49410242 | 6
out kj | Energy equivalent | kJ/mol | q * 96.4853321233 | 3