# 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. From energy conservation of the simple reaction,

$a+X\rightarrow Y+b$

one finds,

$m_a c^2 + K_a + m_X c^2 + K_X = m_Y c^2 + K_Y + m_b c^2 + K_b$

where K is the kinetic energy and m is the rest mass. Rewriting the expression above as

$\left(m_a+m_X - m_b - m_Y\right) c^2 = K_b + K_Y - K_a - K_X$

enables the general definition of Q:

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

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]

Q values are also featured in particle physics. For example in Sargent's rule, which states that the reaction rate of weak interactions is proportional to Q5. The Q value is the kinetic energy released in the decay of the particle at rest. For example, for neutron decay:[2]

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

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.