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Q38P

Expert-verified
Found in: Page 1332

Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

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

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

See the step by step solution

Step 1: Write the given data

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

Step 2: 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)

Step 3: 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:

$Q=2{Q}_{1}+2{Q}_{2}+2{Q}_{3}+{Q}_{4}\phantom{\rule{0ex}{0ex}}=2\left(0.42MeV+1.02MeV+5.49MeV\right)+12.86MeV\phantom{\rule{0ex}{0ex}}=26.7MeV$

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