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Q values of Nuclear Reactions : Nuclear Physics

Here we discuss a mathematical interpretation of the Q values of nuclear reactions. In a nuclear reaction, not only the atomic number and mass number is conserved but also total energy remains conserved. Let us consider the nuclear reaction :
                                                           X + a  ———>  Y + b      ……..(i) 
 
Let Mx, Ma, My & Mb be the rest masses of X, a, Y and b respectively & Ea, Ey and Eb be the kinetic energy of a, Y and b respectively. The target nucleus X is initially at rest, so it has no kinetic energy.
By the conservation of total energy, the equation (i)  can be written as :
Let Q be the energy released or absorbed during the nuclear reaction. It is the difference between the kinetic energy of the product of reaction & that of the initial interacting particle. i.e.
From eqn. (ii) we have :
Reactions for which Q is positive called exothermic reaction & reactions for which Q is negative called endothermic reactions. This is how we have mathematically discussed Q values of nuclear reactions.
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