When hydrogen nuclei are able to overcome the coulomb forces, two protons collide. As a result, one of them decays into a neutron and a positron and electron neutrino are emitted. However, isn't mass gained in this scenario because the the sum of the mass of a proton and neutron is larger than the sum of two protons?

Deja Bradshaw

Deja Bradshaw

Answered question

2022-10-28

When hydrogen nuclei are able to overcome the coulomb forces, two protons collide. As a result, one of them decays into a neutron and a positron and electron neutrino are emitted. However, isn't mass gained in this scenario because the the sum of the mass of a proton and neutron is larger than the sum of two protons?

Answer & Explanation

amilazamiyn

amilazamiyn

Beginner2022-10-29Added 14 answers

The mass of the deuteron is less than the mass of two protons.
The deuterium atom has mass excess of 13.14 MeV, while a hydrogen atom has mass excess 7.29 MeV. (Source. These values are for neutral atoms, which include the 0.51 MeV electron.) So in the reaction
p + p d + e + + ν e , \rm p + p \to d + e^+ + \nu_e,
we have an initial mass excess of 13.56 MeV changing to a final of only 13.14 MeV. The remaining 0.42 MeV is available as extra kinetic energy for the reaction products.
Note also that a free neutron and free proton together are also more massive than the deuteron, by about 2.2 MeV. That's why the deuteron is stable against dissociation.

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