Consider the nuclear reaction ${ } _ { 7 } ^ { 14 } \mathrm {~N} + { } _ { 2 } ^ { 4 } \mathrm { He } \rightarrow { } _ { 8 } ^ { 17 } \mathrm { O } + { } _ { 1 } ^ { 1 } \mathrm { H }$. The known atomic masses are ${ } _ { 7 } ^ { 14 } \mathrm {~N} : \quad 14.003074 \mathrm { u }$
${ } _ { 2 } ^ { 4 } \mathrm { He } : \quad 4.002603 \mathrm { u }$
${ } _ { 1 } ^ { 1 } \mathrm { H } : \quad 1.007825 \mathrm { u }$
${ } _ { 8 } ^ { 17 } \mathrm { O } : \quad 16.999131 \mathrm { u }$
What is the Q-value (or reaction energy) of this reaction? $\left( 1 \mathrm { u } = 931.5 \mathrm { MeV } / c ^ { 2 } \right)$

Question

Quizplus · Accepted Answer

The Q-value of a nuclear reaction is calculated by finding the difference in mass between the reactants and products and then converting this mass difference into energy using Einstein's equation $E=mc^2$. For the given reaction, the mass of the reactants is $14.003074 \, \mathrm{u} + 4.002603 \, \mathrm{u} = 18.005677 \, \mathrm{u}$, and the mass of the products is $16.999131 \, \mathrm{u} + 1.007825 \, \mathrm{u} = 18.006956 \, \mathrm{u}$. The mass difference is $18.005677 \, \mathrm{u} - 18.006956 \, \mathrm{u} = -0.001279 \, \mathrm{u}$. Converting this mass difference to energy gives $-0.001279 \, \mathrm{u} \times 931.5 \, \mathrm{MeV/u} = -1.191 \, \mathrm{MeV}$, indicating that the reaction releases 1.191 MeV of energy.

Consider the Nuclear Reaction the Known Atomic Masses Are 714 N:14.003074u{ } _ { 7 } ^ { 14 } \mathrm {~N} : \quad 14.003074 \mathrm { u }714​ N:14.003074u

Consider the Nuclear Reaction the Known Atomic Masses Are ${ } _ { 7 } ^ { 14 } \mathrm {~N} : \quad 14.003074 \mathrm { u }$