When does electron capture occur instead of positron emission?

1 Answer
Oct 3, 2015

Answer:

Electron capture occurs when the loss in mass is less than that of two electrons.

Explanation:

Nuclear stability depends on the neutron:proton ratio.

Band of Stability
(from www.slideshare.net)

Nuclei that have a neutron: proton ratio that is too low can become stable by positron emission or by electron capture.

1. Positron emission

In positron emission, a proton is converted to a neutron by emitting a positron and a neutrino.

For example,

#""_12^23"Mg" → ""_11^23"Na" + ""_1^0e + ν#

Positron emission occurs spontaneously when the mass of the parent atom is greater than the mass of the daughter atom plus two electrons:

#underbrace(m[""^"A""Z"])_color(red)("parent atom") > underbrace(m[""^"A"("Z"-1)])_color(red)("daughter atom") + underbrace(2m[""_(-1)^0e])_color(red)("2 electrons")#

2. Electron capture

In electron capture, an outside electron is pulled inside the nucleus and combined with a proton to make a neutron, emitting only a neutrino.

For example,

#""_92^231"U" + ""_(-1)^0e → ""_91^231"Pa" + ν#

Electron capture happens most often in the heavier neutron-deficient elements where the mass change is smaller than that from positron emission.

#underbrace(m[""^"A""Z"])_color(red)("parent atom") > underbrace(m[""^"A"("Z"-1)])_color(red)("daughter atom") #

When the loss in mass is less than that of two electrons, positron emission cannot occur, but electron capture will still be spontaneous.