For reactions in which there is an increase in the kinetic energy of the products, Q is positive. The positive Q reactions are said to be exothermic (or exergic). There is a net release of energy since the kinetic energy of the final state is greater than the kinetic energy of the initial state.
For reactions in which there is a decrease in the kinetic energy of the products, Q is negative. The negative Q reactions are endothermic (or endoergic), and they require net energy input.
The Q-value of this reaction is given by:
Q = [ma + mA – (mb + mB)]c2
which is the same as the excess kinetic energy of the final products:
Q = Tfinal – Tinitial
= Tb + TB – (Ta + TA)
See also: Q-value Calculator
See also: E=mc2
Exothermic Reactions
The DT fusion reaction of deuterium and tritium is particularly interesting because of its potential of providing energy for the future. Calculate the reaction Q-value.
3T (d, n) 4He
The atom masses of the reactants and products are:
m(3T) = 3.0160 amu
m(2D) = 2.0141 amu
m(1n) = 1.0087 amu
m(4He) = 4.0026 amu
Using the mass-energy equivalence, we get the Q-value of this reaction as:
Q = {(3.0160+2.0141) [amu] – (1.0087+4.0026) [amu]} x 931.481 [MeV/amu]
= 0.0188 x 931.481 = 17.5 MeV
Tritium is a byproduct of nuclear reactors. Most of the tritium produced in nuclear power plants stems from boric acid, commonly used as a chemical shim to compensate for an excess of initial reactivity. The main reaction in which the tritium is generated from boron is below:
10B(n,2*alpha)T
This neutron reaction with an isotope 10B is the main way radioactive tritium in the primary circuit of all PWRs is generated. Note that this reaction is a threshold reaction due to its cross-section.
Calculate the reaction Q-value.
The atom masses of the reactants and products are:
m(10B) = 10.01294 amu
m(1n) = 1.00866 amu
m(3T) = 3.01604 amu
m(4He) = 4.0026 amu
Using the mass-energy equivalence, we get the Q-value of this reaction as:
Q = {(10.0129+1.00866) [amu] – (3.01604+2 x 4.0026) [amu]} x 931.481 [MeV/amu]
= 0.00036 x 931.481 = 0.335 MeV
Endothermic Reactions
A high-energy photon (gamma-ray) can, under certain conditions, eject a neutron from a nucleus. It occurs when its energy exceeds the binding energy of the neutron in the nucleus. Most nuclei have binding energies in excess of 6 MeV, above the energy of most gamma rays from fission. On the other hand, there are few nuclei with sufficiently low binding energy are of practical interest. These are 2D, 9Be, 6Li, 7Li, and 13C. As can be seen from the table, the lowest threshold have 9Be with 1.666 MeV and 2D with 2.226 MeV.
threshold energies.
In the case of deuterium, neutrons can be produced by the interaction of gamma rays (with a minimum energy of 2.22 MeV) with deuterium:
The reaction Q-value is calculated below:
The atom masses of the reactant and products are:
m(2D) = 2.01363 amu
m(1n) = 1.00866 amu
m(1H) = 1.00728 amu
Using the mass-energy equivalence, we get the Q-value of this reaction as:
Q = {2.01363 [amu] – (1.00866+1.00728) [amu]} x 931.481 [MeV/amu]
= -0.00231 x 931.481 = -2.15 MeV