Nuclear Reaction
The nuclear reaction is written as
a + X → Y + b
The particles a and b may be elementary particles. This transmutation equation does not cover all the reactions because more than one particle may merge.
The most general nuclear transmutation equation can be written as
X + a
X* + x
a + X → Y + b - - - - - - - - - - (1)
Z + c etcIf this is helpful for you then join us for latest updates and continue your learning with us. Thanks. Happy learning
Scattering Nuclear Reaction
The reaction in which emerging particle is of the same kind as the projectile particle is called nuclear scattering reaction.
The first two reactions given in eq(1) are called scattering reactions. The first reaction is called elastic scattering reaction because total kinetic energy of the system is same before collision and after collision.
a + X → X + a
The example of elastic scattering reaction is
1H1 + 6C12 → 6C12 + 1H1 Inelastic Scattering Nuclear Reaction
The inelastic scattering does not follow the conservation of momentum and kinetic energy. The projectile particles loose some of its kinetic energy inside the target through some internal process and only a fraction of it goes into moving the whole target.
The second reaction given in eq(1) is called inelastic scattering in which target nucleus X is raised into excited state. The total kinetic energy of the system is decreased by the amount o the excitation energy given to the target nucleus.
a + X → X* + a
The other reactions given in eq(1) represent different possible nuclear transmutations. The product nuclei in these transmutations may be formed in their ground states or in excited states. The excited product nucleus decays very rapidly to the ground state with the emission of 𝜸- rays.
The fact that product nucleus in a transmutation process can be left in an excited state was discovered by measuring the energies of the protons in (𝝰, p) reactions on light elements. The one or more groups of protons(each containing particles of the same energy) was observed for a particular direction of emission when a given light element was bombarded with mono-energetic natural 𝝰-particles. The existence of the distinct proton groups was demonstrated by their different ranges.
The Q-value can be calculated either from energy difference or from mass difference. The proton group with the greatest energy gives the greatest Q-value. This value corresponds to ground state of the product nucleus. The proton group of lower energy gives a lower Q-value and difference between greatest Q-value and lower Q-value gives the excitation energy of the product nucleus.
Consider an aluminum foil is bombarded with 7.3 MeV 𝝰-particles. The four groups of protons are observed in air with ranges of 101.6cm, 60.8cm, 40.8cm, and 25cm respectively.
2He4 + 13Al27 → [15P31 ] → 14Si30 + 1H1 + Q
The corresponding energies obtained from range energy curves for protons are 9.34MeV, 6.98MeV, 5.55MeV, and 4.2MeV.
The greatest proton energy gives Q = 2.22 MeV which corresponds to the formation of Si30 in its ground state.
The three lower energy proton groups give Q-values of -0.06MeV, -1.44MeV, and -2.4MeV respectively. There are three excited states of Si30 with energies 2.28MeV, 3.66MeV, and 4.6MeV above the ground state.
The ground state energy is taken as the zero point of the energy scale for the various states. 