One of the fusion reactions that occurs in the sun is:
$${ } _ { 2 } ^ { 3 } \mathrm { He } + { } _ { 2 } ^ { 3 } \mathrm { He } \rightarrow { } _ { 2 } ^ { 4 } \mathrm { He } + { } _ { 1 } ^ { 1 } \mathrm { H } + { } _ { 1 } ^ { 1 } \mathrm { H }$$
The following atomic masses are known:
${ } _ { 1 } ^ { 1 } \mathrm { H } : \quad 1.007825 \mathrm { u }$
${ } _ { 2 } ^ { 3 } \mathrm { He } : \quad 3.016029 \mathrm { u }$
${ } _ { 2 } ^ { 4 } \mathrm { He } : \quad 4.002603 \mathrm { u }$
What is the reaction energy released in this fusion reaction? $\left( 1 \mathrm { u } = 931.5 \mathrm { MeV } / \mathrm { c } ^ { 2 } \right)$
A) $19 \mathrm { MeV }$
B) $13 \mathrm { MeV }$
C) $15 \mathrm { MeV }$
D) $11 \mathrm { MeV }$
E) $17 \mathrm { MeV }$

Question

Quizplus · Accepted Answer

The reaction energy released can be calculated by finding the mass difference between the reactants and products and then converting that mass difference into energy using $E = \Delta m c^2$, where $1 \mathrm{u} = 931.5 \mathrm{MeV}/c^2$. The mass of the reactants is $2 \times 3.016029 \mathrm{u} = 6.032058 \mathrm{u}$, and the mass of the products is $4.002603 \mathrm{u} + 2 \times 1.007825 \mathrm{u} = 6.018253 \mathrm{u}$. The mass difference is $6.032058 \mathrm{u} - 6.018253 \mathrm{u} = 0.013805 \mathrm{u}$, which corresponds to an energy release of $0.013805 \mathrm{u} \times 931.5 \mathrm{MeV}/\mathrm{u} = 12.86 \mathrm{MeV}$, which rounds to $13 \mathrm{MeV}$.

One of the Fusion Reactions That Occurs in the Sun