Discuss Conservation Laws of Nuclear Reactions in detail.

 Nuclear Reaction

Definition 

          " The process in which two nuclei collide to produce different products is called nuclear reaction."

If the particles collide and separate without changing then it is called elastic collision rather than a reaction. The two general kinds of nuclear reactions called radioactive nuclear decay and nuclear transmutation reaction. 

           The general nuclear reaction X(a, b)Y is written as 

                                          a   +    X    →    Y    +   b 

           Conservation laws of nuclear reaction is described below.

Conservation Laws of Nuclear Reaction:-

Statement

          "Conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves." 

Conservation laws followed in nuclear reactions are;

1. Conservation of charge
2. Conservation of mass number/nucleons
3. Conservation of linear momentum and angular momentum 
4. Conservation of energy 
5. Conservation of parity 
6. Conservation of isotopic spin

         Now we discuss these laws one by one. Please subscribe to get amazing information. 

1. Law of Conservation of Charge(Z)

          " The total charge on reactant side is equal to total charge on product side is called law of conservation of charge."

Example

                                                ₂He⁴  + ₇N¹⁴ →   ₈O¹⁷  + ₁H¹ 

Charge on reactant  = 2 + 7 = 9

Charge on product  = 8 + 1 = 9 

2. Law of Conservation of Nucleons/Mass Number(A)

          " The total number of nucleons on reactant side is equal to total number of nucleons on product side is called law of conservation of nucleons." This law does not hold at low energies. 

Example

                                       ₂He⁴  + ₇N¹⁴ →   ₈O¹⁷  + ₁H¹ 

Nucleons on reactant  = 4 + 14 = 18

Nucleons on product  = 17 + 1 = 18

3. Law of Conservation of Energy

          " The energy of interacting particle remains conserved in a closed system is called law of conservation of energy or law of conservation of mass-energy."

          The law of mass-energy forced the physicists to accept the existence of neutrino in beta decay. 

           Consider a projectile nucleus "a" having kinetic energy  E_a and mass m_a is incident on rest target nucleus "X" having mass m_x . The target nucleus "X" has no kinetic energy because it is at rest.

                   The product nucleus "Y" is generated after nuclear reaction has kinetic energy E_y and mass m_y. The emerging nucleus "b" is generated after nuclear reaction has kinetic energy E_b and mass m_b. 

 

                  The law of mass energy is given as 

                                    ∑ (KE + mc² ) = Constant

                  The nuclear reaction is 

          

                                     a + X  ⟶  Y + b

                

                 (m_a c²  + E_a) + (m_x c²  + 0 )   =  (m_y c²  + E_y ) + (m_b c²  + E_b)

                 (m_a + m_x)c² - (m_y+ m_b )c²   =  E_y + E_{b -} E_a

                 (m_a + m_x)c² - (m_y+ m_b )c²   = Q

            

          Where Q =  E_y + E_b  - E_a   is the difference between the kinetic energy of products of nuclear reaction and kinetic energy of reactant particles. It is called Q-value of nuclear reaction. 

                     Q =  E_y + E_b  - E_a   

4. Law of Conservation of Linear Momentum

          "The total momentum is constant before and after nuclear reaction  in an isolated system is called law of conservation of linear momentum."

          Consider a projectile nucleus "a" having velocity  V_a and mass m_a is incident on rest target nucleus "X" having mass m_x . 

          The product nucleus "Y" is generated after nuclear reaction has velocity V_y and mass m_y. The emerging nucleus "b" is generated after nuclear reaction has velocity V_b and mass m_b. 

          The law of conservation of linear momentum is given as

                                        ⅀mV = Constant

                      The nuclear reaction is 

                                   a + X  ⟶  Y + b

                           m_a V_a  + 0   =   m_y V_y   + m_b V_b  

                                m_a V_a     =   m_y V_y   + m_b V_b  

5. Law of Conservation of Angular Momentum and Spin

          " This law states that total angular momentum and spin should be conserved before and after nuclear reaction." 

                                 ⅀L  = Constant 

          This law helps us to assign values of angular momentum and spin to emitted particles.

6. Law of Conservation of Parity

          " The net parity before nuclear reaction is equal to net parity after nuclear reaction is called law of conservation of parity." 

             If the parity is odd before nuclear reaction then it will also be odd after nuclear reaction. The parity holds for strong nuclear reaction but not for weak nuclear reaction. 

          The parity of nuclear reaction is given as P = (-1)^ℓ 

          The parity is even when ℓ is even and parity is odd when ℓ is odd. 

7. Law of Conservation of Isotopic Spin

          The isotopic spin is a quantum number related to its strong interaction. The particles that are affected equally by the strong force but have different charges( e.g. protons and neutrons) can be treated as being of different states of the same particles with isospin values related to the of charge states.

          The idea of charge independent nuclear force leads to a new term called isotopic spin. According to this term neutron and proton are the different states of nucleon.

          The isotopic spin variable was assigned values +1/2 for neutron and -1/2 for proton. So there exists an isotopic spin quantum number having magnitude `\sqrt{T\left(T+1\right)}` ħ for each type of fundamental particle. 

       This law states that net isotopic spin should be equal before nuclear reaction and after nuclear reaction.