Q-Value Calculator for Nuclear Reactions
Compute the Q-value of a nuclear reaction from reactant and product masses, binding energies, or mass excess values. See whether the reaction is exothermic or endothermic and convert between MeV and joules.
Quick examples
What is the Q-value of a nuclear reaction?
In nuclear physics, the Q-value of a reaction is the net amount of energy released or absorbed when reactants transform into products. It is defined as the difference in total rest mass energy between the initial and final states:
\[ Q = \left(\sum_i m_{\text{reactants},i} - \sum_j m_{\text{products},j}\right)c^2 \]
- Q > 0: exothermic reaction – energy is released.
- Q < 0: endothermic reaction – energy must be supplied.
Because nuclear masses are usually tabulated in atomic mass units (u), it is convenient to use the conversion
\[ 1\ \text{u} = 931.494\ \text{MeV}/c^2 \]
so that the Q-value in MeV can be computed directly from mass differences in u.
Formulas used in this calculator
1. From atomic or nuclear masses
If you enter masses in atomic mass units (u), the calculator uses
\[ Q(\text{MeV}) = \left(\sum_i m_{\text{reactants},i} - \sum_j m_{\text{products},j}\right)\times 931.494\ \text{MeV} \]
The sign convention is:
- \(Q > 0\): products are more tightly bound (lower total mass) than reactants.
- \(Q < 0\): products are less tightly bound (higher total mass) than reactants.
2. From binding energies
The binding energy \(B\) of a nucleus is the energy required to disassemble it into free nucleons. For a reaction
\[ \sum_i A_i \rightarrow \sum_j B_j \]
the Q-value in MeV can be written as
\[ Q = \sum_j B(B_j) - \sum_i B(A_i) \]
i.e. the difference between total binding energy of products and reactants.
3. From mass excess
Nuclear data tables often list the mass excess \(\Delta\) instead of the absolute mass. For a nucleus with mass number \(A\):
\[ \Delta = M c^2 - A u c^2 \]
For a reaction, the Q-value in MeV is
\[ Q = -\left(\sum_i \Delta_{\text{reactants},i} - \sum_j \Delta_{\text{products},j}\right) \]
The calculator implements this formula when you choose the “Mass excess” mode.
4. Converting MeV to joules
If you select joules as the output unit, the calculator uses
\[ 1\ \text{MeV} = 1.602176634\times 10^{-13}\ \text{J} \]
Worked example: D–T fusion
Consider the fusion reaction
\[ ^2\text{H} + ^3\text{H} \rightarrow ^4\text{He} + n \]
Using approximate atomic masses (in u):
- \(m(^2\text{H}) = 2.014102\)
- \(m(^3\text{H}) = 3.016049\)
- \(m(^4\text{He}) = 4.002603\)
- \(m(n) = 1.008665\)
Compute the mass difference:
\[ \Delta m = (2.014102 + 3.016049) - (4.002603 + 1.008665) = 5.030151 - 5.011268 = 0.018883\ \text{u} \]
Convert to energy:
\[ Q = 0.018883\times 931.494 \approx 17.6\ \text{MeV} \]
The positive Q-value indicates an exothermic reaction: about 17.6 MeV of energy is released per fusion event.
Common pitfalls and best practices
- Be consistent with mass type. Do not mix atomic and nuclear masses in the same calculation.
- Include all particles. Remember to include incident neutrons, emitted neutrons, and gamma rays (if you are using binding energies).
- Use precise data. For research work, take masses or mass excess values from a trusted database such as AME2020 or NNDC.
- Check conservation laws. Ensure that total charge and nucleon number are conserved in the reaction you enter.
Q-value calculator FAQ
What is the physical meaning of a positive or negative Q-value?
A positive Q-value means the products have lower total rest mass than the reactants. The mass difference appears as released energy (exothermic reaction). A negative Q-value means the reaction absorbs energy: you must supply at least \(|Q|\) to make it proceed (endothermic reaction).
Should I use atomic or nuclear masses?
You can use either, as long as you are consistent. Atomic masses include electrons; nuclear masses do not. For most nuclear reactions that conserve the total number of electrons (no beta decay), atomic masses are convenient and widely tabulated. If electrons change (e.g., beta decay), it is safer to work with nuclear masses or correct explicitly for electron masses.
Where can I find accurate mass or mass-excess data?
Standard references include the Atomic Mass Evaluation (AME2020), the National Nuclear Data Center (NNDC) at BNL, and the IAEA Nuclear Data Services. These sources provide atomic masses, nuclear masses, binding energies, and mass excess values with uncertainties.
Does this calculator handle reaction thresholds and kinematics?
This tool focuses on the rest-mass Q-value only. It does not compute threshold energies in the lab frame, angular distributions, or detailed kinematics. For threshold calculations, you must combine the Q-value with conservation of momentum in the appropriate reference frame.