91Ó°ÊÓ

The expression for energy is given by,

$\mathit{Q}\mathbf{=}\mathbf{-}\mathbf{∆}\mathit{m}{\mathit{c}}^{\mathbf{2}}$

Here, is the energy release in a reaction,$\mathbf{∆}\mathit{m}$ is the mass difference between the parent nuclei and the daughter nuclei, and c is the velocity of light.

If can be carefully observed thatin the carbon-carbon cycle, the products are two positrons$\left(2e^{+}\right)$ , two neutrinos$\left(2v\right)$ , and one helium nucleus$\left({}^{4}He\right)$ .

The same products are also obtained in the proton-proton cycle.

Therefore, the carbon cycle is exactly equivalent to proton-proton cycle.

The value of the energy is the sum of the Q values of the carbon cycle.

$$\begin{gathered} Q_c=\underset{n=1}{\overset{6}{∑}}{Q}_n \\ =Q_1+Q_2+Q_3+Q_4+Q_5+Q_6 \\ =1.95Mev+1.19Mev+7.55Mev+7.30Mev+1/73Mev+4.97Mev \\ =24.7Mev \end{gathered}$$

The Q value is same for both cycles.

Therefore, it is verified that the two cycles have the same Q value.