Question

We have seen that Qfor the overall proton–proton fusion cycle is 26.7 MeV. How can you relate this number to the Qvalues for the reactions that make up this cycle, as displayed in Fig. 43-11?

Short answer

The given Q-value 26.7 MeV is the total energy of the proton-proton fusion cycle.

Step-by-step solution

Write the given data

The Q-values for the individual reactions of the proton-proton fusion cycle in figure 43-11 are given.

Determine the concept of Q-value

The Q-value of the fusion process is the amount of energy that is either absorbed or released during the process. Thus, it describes the integration process for a fusion process that involves the binding of two nuclei.

Formula:

The Q-value of a given full cycle is the sum of all the energy (or Q-value) of the reactions that contribute to the full cycle reaction as follows:

$Q=\sum _i^n{Q}_i$ …… (i)

Calculate the Q-value of the overall proton-proton fusion cycle

Let, the Q-values of all the given individual reactions be $Q_1=0.42MeV$,$Q_2=1.02MeV$$Q_3=5.49MeV$ and $Q_4=12.86MeV$. Thus, for the overall proton-proton fusion cycle, the total Q-value can be calculated using equation (i) as follows:

$$\begin{gathered} Q=2Q_1+2Q_2+2Q_3+Q_4 \\ =2\left(0.42MeV+1.02MeV+5.49MeV\right)+12.86MeV \\ =26.7MeV \end{gathered}$$

Hence, the given value 26.7 MeV is the total energy of the proton-proton fusion cycle.