# Q value (nuclear science)

For other uses, see Q value.

In nuclear physics and chemistry, the Q value for a reaction is the amount of energy released by that 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. Q values affect reaction rates[how?].

## Definition

Considering the energy conservation of the simple reaction, enables the general definition of Q based on mass-energy equivalence, where K is kinetic energy and m is mass:

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

A reaction with a positive Q 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 Q 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.[1]

## Applications

Chemical Q 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).

Q values are also featured in particle physics. For example, Sargent's rule states that weak reaction rates are proportional to Q5. The Q 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:[2]

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

where mn is the mass of the neutron, mp is the mass of the proton, mν is the mass of the electron antineutrino and me is the mass of the electron; and the K are the corresponding kinetic energies. The neutron has no initial kinetic energy since it is at rest. In beta decay, a typical Q is around 1 MeV.

The decay energy is divided among the products in a continuous distribution for more than 2 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 upcoming KATRIN experiment.