Q value (nuclear science)#Applications

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

: $Q\; =\; K\_\backslash text\{f\}\; -\; K\_\backslash text\{i\}\; =\; (m\_\backslash text\{i\}\; -\; m\_\backslash text\{f\})\; \backslash ,\; c^2,$

where {{mvar|K}} denotes the kinetic energy of the mass {{mvar|m}}.

A reaction with a positive {{mvar|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 {{mvar|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.

{{cite book

|first=K. S. |last=Krane

|year=1988

|title=Introductory Nuclear Physics

|page=381

|publisher=John Wiley & Sons

|isbn=978-0-471-80553-3

}} Observe that a chemical reaction is exothermic when it has a negative enthalpy of reaction, in contrast a positive {{mvar|Q}} value in a nuclear reaction.

The {{mvar|Q}} value can also be expressed in terms of the Mass excess $\backslash Delta\; M$ of the nuclear species as

: $Q\; =\; \backslash Delta\; M\_\backslash text\{i\}\; -\; \backslash Delta\; M\_\backslash text\{f\}.$

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

Chemical {{mvar|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).

{{mvar|Q}} values are also featured in particle physics. For example, Sargent's rule states that weak reaction rates are proportional to {{mvar|Q}}⁵. The {{mvar|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:

{{cite book

|first1=B. R. |last1=Martin

|first2=G. |last2=Shaw

|year=2007

|title=Particle Physics

|page=[https://archive.org/details/particlephysics0000mart_k5d4/page/34 34]

|publisher=John Wiley & Sons

|isbn=978-0-471-97285-3

|url=https://archive.org/details/particlephysics0000mart_k5d4/page/34

}}

: $$

Q = (m_\text{n} - m_\text{p} - m_{\overline\nu} - m_\text{e}) c^2 =

K_\text{p} + K_\text{e} + K_{\overline\nu} = 0.782~\text{MeV},

where m_n is the mass of the neutron, {{mvar|m}}_p is the mass of the proton, {{mvar|m}}_{{{overline|{{math|ν}} }}} is the mass of the electron antineutrino, {{mvar|m}}_e is the mass of the electron, and the {{mvar|K}} are the corresponding kinetic energies. The neutron has no initial kinetic energy since it is at rest. In beta decay, a typical {{mvar|Q}} 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 spectra to search for neutrinoless decay and neutrino mass; this is the principle of the ongoing KATRIN experiment.

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

{{reflist|25em}}

• {{cite web |title=Query input form |series=Nuclear Structure and Decay Data |publisher=IAEA |url=http://www-nds.iaea.org/queryensdf}} – interactive query form for {{mvar|Q}}-value of requested decay.
• {{cite web |first=Eugenio |last=Schuster |date=Fall 2020 |title=Nuclear energy release; fusion reactions |id=ME 362 Lecture 1 |series=Mechanical Engineering 362 – Nuclear Fusion and Radiation |publisher=Lehigh University |place=Bethlehem, PA |url=https://www.lehigh.edu/~eus204/teaching/ME362/lectures/lecture01.pdf |access-date=2021-03-05}} – demonstrates simply the mass-energy equivalence.

Category:Nuclear physics

Category:Energy