The reaction .^13_6C(d, p)^14_6C has Q-value of 5.952 Me V and a resonance when

Question

The reaction .^13_6C(d, p)^14_6C has Q-value of 5.952 Me V and a resonance when the incident deuteron has a laboratory energy of 2.45 MeV The reaction ^11 5_B(alpha, n)^14_7N, Q=0.158 MeV will also have a resonance. Explain why and estimate the laboratory kinetic energy of the alpha-particle at which it would occur. The following pieces of information are needed to answer: 1 . The beta-decay 14^6_C rightarrow 14^7_N +e^- + v, has Q-value of 0. 156 MeV 2. The neutron-hydrogen atom mass difference is 0.782 MeV/c^2

Explanation / Answer

Mass of C-13 = 13.003355 u

mass of D = 2.014102 u

KE of the D = 2.45 Mev

mas of P = 1.007825 u

mass of C-14 = 14.003242

u = 931.494 Mev/c2

Q-value of the reaction = (13.003355 + 2.014102) *931.494 - (14.003242 + 1.007825) *931.494 Mev

                                      = 5.952 Mev

The resonance occurs beacuse the compund nucleus C-15 energy level at 2.45 Mev, incident neutron will excite it to the energy level.

Mass of B-11 = 11.009306 u

      (alpha) He-4   = 4.002603 u

                     n =   1.008665 u

     N-14 = 14.003242 u

      Q - value of the reaction = (11.009306 + 4.002603) *931.494 - (14.003242 + 1.008665) *931.494

                                               = -5.0496 Mev

The reaction has -ve Q-value, for the reaction to procced the alpha - particle must have the minimum energy of 5.0496 Mev

For the raction to occur the labarotary energy of the alpha particle = 5.0496 + 0.158 = 5.208 Mev

C-14 -> N-14 +e + u masses of electron and nutrino are negligible

Q-value = 14.003242 - 14.003074) *931.494 = 0.156 Mev

H- atom mass = 1.007825 u

               n = 1.008665 u

mass difference = (1.008665 - 1.007825) *931.494 = 0.782 Mev

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