Q value (nuclear science) explained

In nuclear physics and chemistry, the 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. values affect reaction rates. In general, the larger the positive value for the reaction, the faster the reaction proceeds, and the more likely the reaction is to "favor" the products.

Q = (m _{r} - m _{p)} x 0.9315GeV where the masses are in atomic mass units. Also, both m _{r} and m _{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

( E _{i} = E _{f} ), enables the general definition of based on the mass–energy equivalence. For any radioactive particle decay, the kinetic energy difference will be given by:Q = K _{f} - K _{i} = (m _{i-} m _{f)} c ^{2} ~ where denotes the kinetic energy of the mass  .A reaction with a positive 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 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] Observe that a chemical reaction is exothermic when it has a negative enthalpy of reaction, in contrast a positive value in a nuclear reaction.\Delta M of the nuclear species as:Q = \Delta M _{i} - \Delta M _{f} ~

Proof: The mass of a nucleus can be written as

M = A u + \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 = \Delta M _{i} - \Delta M _{f} ~ .

Applications

Chemical 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).

values are also featured in particle physics. For example, Sargent's rule states that weak reaction rates are proportional to ⁵. The 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 _{n} - m _{p} - m _{\overline{\nu} } - m_\text)c^2 = K_\text + K_\text + K_ = \textwhere m_n is the mass of the neutron, _p is the mass of the proton, is the mass of the electron antineutrino, and _e is the mass of the electron; and the are the corresponding kinetic energies. The neutron has no initial kinetic energy since it is at rest. In beta decay, a typical 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

• Web site: Query input form . Nuclear Structure and Decay Data . . – interactive query form for -value of requested decay.
• Web site: Eugenio . Schuster . Fall 2020 . Nuclear energy release; fusion reactions . ME 362 Lecture 1 . Mechanical Engineering 362 – Nuclear Fusion and Radiation . . Bethlehem, PA . 2021-03-05. – demonstrates simply the mass-energy equivalence.

Notes and References

1. Book: Krane , K.S. . 1988 . Introductory Nuclear Physics . 381 . . 978-0-471-80553-3.
2. Book: B.R. . Martin . G. . Shaw . 2007 . Particle Physics . 34 . . 978-0-471-97285-3 .