Chain It Out!!!!!

The energy radiated by the sun is generated primarily by the fusion of Hydrogen into helium-4 (He) In stars of size in the order of that of the sun, the primary mechanism by which fusion takes place is the proton-proton chain.The chain reactions begin with the following reactions;

\[2p\rightarrow X_{1}+e^{+}+X_{2} \]......(0.42MeV), \[p+X_{1}\rightarrow X_{3}+\gamma \]....(5.49MeV)

The amount listed in the parenthesis in the above reactions are the total kinetic energy carried by the products, including gamma rays. Here p denotes a proton,e+ denotes a positron, gamma denotes gamma rays, and X1, X2, and X3 denote the particles that you have to identify. The density of electrons in the core of the sun is sufficient so that the positron is annihilated almost immediately, releasing energy x,

\[e^{+}+e^{-}\rightarrow2\gamma \]....(x)

Subsequently, two major processes occur simultaneously that we call pp1 and pp2 branches

The pp1 branch is the following single reaction which releases an energy y\[2X_{3}\rightarrow^{4}He+2X_{4} \]....(y)

The branch pp2 consists of the following three reactions.

\[X_{3}+^{4}He\rightarrow X_{5}+\gamma \]

\[X_{5}+e^{-}\rightarrow X_{6}+X_{7} \]....(z)

z is the energy released in second step of these three reactions.

\[X_{6}+X_{4}\rightarrow2*^{4}He \]

The energy released in the production of one helium-4 nucleus, including the kinetic energy of all products and all energy carried by gamma rays is w.

the second reaction of pp2 does not occur because there is insufficient energy. The constraint it places on the value of z is (z<a) x,y,z,w,a are all in MeV

Find (x+y+a+w). Round the answer to the nearest integer. Details and assumptions:

-mass of the electron is 0.51MeV/c^2

-mass of proton is 938.27MeV/c^2

-mass of helium-4 nucleus is 3727.38MeV/c^2


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