Q value (nuclear science)

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.

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:

$Q = K_{(\text{Final})} - K_{(\text{Initial})} = (m_{Initial}- m_{Final})c^2$

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]

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

where m_n is the mass of the neutron, m_p is the mass of the proton, m_ν is the mass of the electron antineutrino and m_e 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.

See also

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

Notes and references

1. K.S. Krane (1988). Introductory Nuclear Physics. John Wiley & Sons. p. 381. ISBN 0-471-80553-X.
2. B.R. Martin and G. Shaw (2007). Particle Physics. John Wiley & Sons. p. 34. ISBN 0-471-97285-1.

External links

• Nuclear Structure and Decay Data – IAEA with query on decays' Q-values