Question

what is the Q-value of the reaction $p+{ }^{7} Li \rightarrow{ }^{4} He +{ }^{4} He$ The atomic masses of ${ }^{1} H ,{ }^{4} He$ and ${ }^{7} Li$ are $1.007825\, u , 4.002603\,u$ and $7.016004\, u$ respectively

• A. 17.35 MeV
• B. 18.06 MeV
• C. 177.35 MeV
• D. 170.35 MeV

Answer 1

Answer: (A)

17.35 MeV

Answer 2

The total energy released in reaction $(Q)$ is equal to the difference in kinetic energy of the final particles and of initial particles.
The total mass of the initial particles
$m_{1}=1.007825+7.016004$
$=8.023829\, u$
and the total mass of final particles
$m_{f}=2 \times 4.002603$
$=8.005206 u$
Difference between initial and final mass of particles
$\Delta m=m_{i}-m_{f}$
$=8.023829-8.005206$
$=0.018623\, u$
The Q-value is given by
$Q=(\Delta m) c^{2}$
$=0.018623 \times 93.15$
$=17.35\, MeV$
Difference between initial and final mass of particles
The $Q$-value is given by