Question

To calculate the total energy released in the proton-proton cycle, considering the overall effect in (1¹H + 1¹H → 2²H + e⁺ + nuₑ), (1¹H + 2²H → 3³He + γ), and (3³He + 3³He → 4⁴He + 1¹H + 1¹H), including annihilation energy:

a) 26.7 MeV
b) 19.77 MeV
c) 32.31 MeV
d) 14.92 MeV

Answer 1

The total energy released in the proton-proton cycle, including the annihilation energy from the emitted positrons, is 26.7 MeV. This value is calculated by considering the energy released in positron emissions, gamma-ray production, and subsequent positron-electron annihilations in the described reactions of the cycle. The correct option is A.

Step-by-step explanation:

The proton-proton cycle is a set of nuclear reactions that power stars like our sun. To calculate the total energy released, we consider the three key reactions in the cycle:

1. 1¹H + 1¹H → 2²H + e+ + νe (positron and neutrino emission)
2. 1¹H + 2²H → 3³He + γ (gamma ray emission)
3. 3³He + 3³He → 4⁴He + 2(1¹H) (two protons released)

When we account for the annihilation energy of emitted positrons with electrons, the total energy released is 26.7 MeV. This includes energy from the positrons emitted and their subsequent annihilation with electrons to form more gamma (γ) rays.