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Nuclei


Physics. 438. 13.1 INTRODUCTION. In the previous chapter, we have learnt that in ... and its constituents, ∆M, is called the mass defect, and is given by ... adding nucleons they will not change the binding energy of a nucleon ... The energy released (the Q value ) in the fission reaction of nuclei like ... Given the mass values:.


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(i) Nuclear reaction ^{1}_{1} H + ^3_1 H \rightarrow ^{2}_{1} H + ^{2}_{1} H

Q value of the nuclear reaction [math] = [ \text{ mass of } ^1_1 H + \text{ mass of } ^3_1 H - \text{ mass of }2(^2_1 H)] c^2 [/math]

Given that

m(^1_1 H) = 1.007825 u

m(^2_1 H) = 2.014102 u

m (^3_1 H) = 3.016049 u


Q -value [math] = [1.007825 + 3.016049 - 2 * 2.014102] c^2 [/math]

Q-value =-0.00433*c^2\ u

Q-value = - 0.00433 * c^2 * 931.4 MeV/c^2                        \because 1 u = 931.4 MeV/c^2

Q-value = -4.0334 MeV

The negative Q value of the reaction indicates an endothermic reaction.


(ii)Nuclear reaction ^{12}_{6} C + ^{12}_6 C \rightarrow ^{20}_{10} Ne + ^{4}_{2} He

Q value of the nuclear reaction [math] = [ \text{ mass of } 2( ^{12}_{6} C ) - \text{ mass of } ^{20}_{10} Ne - \text{ mass of } (^4_2 He)] c^2 [/math]

Given that

m(^{12}_6 C) = 12 u

m(^{20}_{10} Ne) = 19.992439 u

m(^{4}_{2} He) = 4.002603 u


Q - value = 2* 12 - 19.992439 - 4.002603] c^2

Q-value = 0.004958 c^2 u

Q-value = 0.004958 c^2 * 931.4 MeV/c^2

Q-value = 4.62 MeV

The positive Q-value of the reaction indicates the exothermic reaction.