Question

Why does electron capture produce a neutrino?

Answer 1

Electron capture produces an electron neutrino in order to conserve lepton numbers.

Electron capture is a process in which one of the inner electrons of an atom is captured by a proton in the nucleus, forming a neutron and emitting an electron neutrino.

`p + e⁻ → n + ν_e`

You are probably familiar with conservation laws like the Law of Conservation of Energy and the Law of Conservation of Momentum. One of the rules that must be followed in nuclear reactions is the Law of Conservation of Lepton Number.

A lepton is an elementary particle with spin ½ that does not undergo strong nuclear forces. Electrons and neutrinos have spin ½ and are outside the nucleus, so they are leptons. The lepton numbers of electrons and of electron neutrinos are +1.

Protons and neutrons are held together in the nucleus by the strong nuclear force. They have lepton numbers of zero.

If the process were simply `p + e⁻ → n`, the sum of the lepton numbers would be +1 on the left and 0 on the right. Lepton numbers would not be conserved.

If an electron neutrino is emitted, as in `p + e⁻ → n + ν_e`, the sums of the lepton numbers are +1 on the left and +1 on the right. Lepton numbers are conserved.

Good presentation, very nice pictures on this website: http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/radact2.html