question for astronomy

Question

The pp-chain is the primary way that stars like the Sun burn hydrogen into helium. It is a sequence of nuclear reactions whose net effect is to turn four protons into a helium nucleus (alpha particle). There are several different branches of the pp-chain, but the first step starts them all: 2p + → D + e + + νe. In this reaction formula, e + is a positron (anti-electron), νe is an electron-neutrino and D is a deuterium nucleus (one proton and one neutron bound together). How much energy is released by this reaction? me = 9.11 × 10−31 kg, mp = 1.67262 × 10−27 kg, mD = 3.34449 × 10−27 kg and mν ≈ 0.

Answer 1

For this problem we need to use Einstein's E=mc² formula. We want to find the change in energy so we need to calculate the initial energy of the two protons and the final energy of the Deuterium and electron. The initial energy is just the sum of the mass of the two protons times c² so 2*(1.67262 x 10^-27)*c² = 2.79766 x 10^-27 kg *c² (we'll keep the units in terms of c² until the end). The final mass is the mass of the Deuterium plus the mass of the positron so 3.3449 x 10^-27 + 9.11 x 10^-31 = 3.3458 x 10^-27. The final energy is then 3.3458 x 10^-27 * c². The difference in energy is the energy that is released in the reaction so E_final - E_initial = (3.3458 x 10^-27)*c² - (2.792766 x 10^-27)*c² = (3.3458 -2.792766)x10^-27 *c² = 0.553034 x 10^-27 * c² = 4.97 x 10^-12 Joules or 31.02 Mega Electron Volts.