Q value (nuclear science)

In nuclear physics and chemistry, the Template:Mvar value for a nuclear reaction is the amount of energy absorbed or released during the reaction. The value relates to the enthalpy of a chemical reaction or the energy of radioactive decay products. It can be determined from the masses of reactants and products. Template:Mvar values affect reaction rates. In general, the larger the positive Template:Mvar value for the reaction, the faster the reaction proceeds, and the more likely the reaction is to "favor" the products.

$Q=(m_{\text{r}}-m_{\text{p}})\times \text{0.9315 GeV }$

where the masses are in atomic mass units. Also, both $m_{\text{r}}$ and $m_{\text{p}}$ are the sums of the reactant and product masses respectively.

Definition

The conservation of energy, between the initial and final energy of a nuclear process $\text{( }{E}_{\text{i}}=E_{\text{f}}\text{ ),}$ enables the general definition of Template:Mvar based on the mass–energy equivalence. For any radioactive particle decay, the kinetic energy difference will be given by:

$Q=K_{\text{f}}-K_{\text{i}}=(m_{\text{i}}-m_{\text{f}})c^2$

where Template:Mvar denotes the kinetic energy of the mass Template:Mvar . A reaction with a positive Template:Mvar value is exothermic, i.e. has a net release of energy, since the kinetic energy of the final state is greater than the kinetic energy of the initial state. A reaction with a negative Template:Mvar value is endothermic, i.e. requires a net energy input, since the kinetic energy of the final state is less than the kinetic energy of the initial state. Observe that a chemical reaction is exothermic when it has a negative enthalpy of reaction, in contrast a positive Template:Mvar value in a nuclear reaction.

The Template:Mvar value can also be expressed in terms of the Mass excess $\mathrm{\Delta }M$ of the nuclear species as:

$Q=\mathrm{\Delta }{M}_{\text{i}}-\mathrm{\Delta }{M}_{\text{f}}$

Proof

The mass of a nucleus can be written as $M=Au+\mathrm{\Delta }M,$ where $A$ is the mass number (sum of number of protons and neutrons) and $u{=}^{12}C/12=931.494$MeV/c$2^{}$. Note that the count of nucleons is conserved in a nuclear reaction. Hence, $A_f=A_i$ and $Q=\mathrm{\Delta }{M}_{\text{i}}-\mathrm{\Delta }{M}_{\text{f}}$.

Applications

Chemical Template:Mvar values are measurement in calorimetry. Exothermic chemical reactions tend to be more spontaneous and can emit light or heat, resulting in runaway feedback(i.e. explosions).

Template:Mvar values are also featured in particle physics. For example, Sargent's rule states that weak reaction rates are proportional to Template:Mvar⁵. The Template:Mvar value is the kinetic energy released in the decay at rest. For neutron decay, some mass disappears as neutrons convert to a proton, electron and antineutrino:

$Q=(m_{\text{n}}-m_{\text{p}}-m_{\bar{\mathrm{\nu }}}-m_{\text{e}})c^2=K_{\text{p}}+K_{\text{e}}+K_{\bar{\nu }}=\text{0.782 MeV ,}$

where m_n is the mass of the neutron, Template:Mvar_p is the mass of the proton, Template:Mvar_{Template:Overline} is the mass of the electron antineutrino, and Template:Mvar_e is the mass of the electron; and the Template:Mvar are the corresponding kinetic energies. The neutron has no initial kinetic energy since it is at rest. In beta decay, a typical Template:Mvar is around 1 MeV.

The decay energy is divided among the products in a continuous distribution for more than two products. Measuring this spectrum allows one to find the mass of a product. Experiments are studying emission spectrums to search for neutrinoless decay and neutrino mass; this is the principle of the ongoing KATRIN experiment.

See also

• Binding energy
• Calorimeter (particle physics)
• Decay energy
• Fusion energy gain factor
• Pandemonium effect

External links

• Template:Cite web – interactive query form for Template:Mvar-value of requested decay.
• Template:Cite web – demonstrates simply the mass-energy equivalence.