By Sunil Bhardwaj

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Those reactions in which nucleus of the atom of an element is involved is known as nuclear reaction. The energy change associated with any nuclear reaction is expressed in terms of one nuclear chemistry factor is known as Q and the value is known as Q - Values. $$ Target + Projectile = Recoil Target + Ejected Particles. $$ As the target is not moving, so it has only one type of energy and it is because of mass \(({ m }_{ 0 }).\) Projectiles have two types of energy one because of mass \(({ m }_{ 1 })\) and other K.E. \(({ E }_{ 1 })\)
\( \therefore \) Total energy of projectile is \(({ m }_{ 1 } + { E }_{ 1 }).\)
Similarly total energy of recoil target is \(({ m }_{ 2 } + { E }_{ 2 })\)
and that of ejected particles will be \(({ m }_{ 3 } + { E }_{ 3 })\)
On substituting these values in above nuclear reaction, we get: $$ ({ m }_{ 0 }) + ({ m }_{ 1 } + { E }_{ 1 }) = ({ m }_{ 2 } + { E }_{ 2 }) + ({ m }_{ 3 } + { E }_{ 3 }) $$ $$ ({ m }_{ 0 } + { m }_{ 1 }) + { E }_{ 1 } = ({ m }_{ 2 } + { m }_{ 3 }) + ({ E }_{ 2 } + { E }_{ 3 }) $$ $$ ({ m }_{ 0 } + { m }_{ 1 }) - ({ m }_{ 2 } + { m }_{ 3 }) = ({ E }_{ 2 } + { E }_{ 3 }) - { E }_{ 1 } $$ But energy of products - Energy of reactant $$ ({ E }_{ 2 } + { E }_{ 3 }) - { E }_{ 1 } $$ is known as Q value,$$ \therefore Q = { m }_{ reactants } - { m }_{ products } = \Delta m (atomic mass unit) $$ $$ \therefore Q = \Delta m \times 931 (MeV) $$ When Q is positive the energy is evolved. The reaction is Exoergic. But when Q is negative the reaction is said to be Endoergic.

Threshold Energy u. Eth : When the Q is negative, the nuclear reaction is said to be endoergic. For endoergic reaction to take place, the energy is to be supplied, now the question is how this energy must be supplied?
As the energy of the target cannot be increased, the only possibility, the energy of projectiles can be increased in the form of acceleration. The part of the energy of the projectiles is utilised for the maintaining the momentum of recoil nucleus. The minimum amount of energy, that is necessary for endoergic reaction is called threshold energy. \(({ E }_{ th }).\) It is found that $$ { E }_{ th } = Q\left[ 1+\frac { { m }_{ P } }{ { m }_{ T } } \right] $$ Where \({ m }_{ P }\) is mass of projectiles and \({ m }_{ T }\) is mass of target.