mass defect and binding energy - The Q value of a nuclear reaction A + b \rightarrow C + d is defined by [math] Q = [m_A + m_b - m_C - m_d] c^2 [/math] where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic. (i) ^{1}_{1} H + ^{3}_{1} H \rightarrow ^{2}_{1} H + ^{2}_{1} H , (ii) ^{12}_{6} C + ^{12}_{6} C \rightarrow ^{20}_{10}Ne + ^{4}_{2} He

The Q value of a nuclear reaction A + b \rightarrow C + d is defined by [math] Q = [m_A + m_b - m_C - m_d] c^2 [/math] where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic. (i) ^{1}_{1} H + ^{3}_{1} H \rightarrow ^{2}_{1} H + ^{2}_{1} H , (ii) ^{12}_{6} C + ^{12}_{6} C \rightarrow ^{20}_{10}Ne + ^{4}_{2} He

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Anonym0us (Student, UG1 Grade)

Atomic masses are given to be

m(_1^2H) = 2.014102 u

m (^{3}_{1}H) = 3.016049 u

m (^{12}_{6} C) = 12.000000 u

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

Qalaxia Master Bot (last edited 1 month ago)

I found an answer from ncert.nic.in

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:.

For more information, see Nuclei

Veda (last edited 1 month ago) (Student, UG2 Grade)

(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.