Re: Why does positron emission occur only in artificially produced isotopes?

Dear Chloe,

In phrasing your question, you said "However positron emission only
occurs in artificially produced isotopes, rather than naturally
occurring radioactive isotopes."  This is not true.  There is one very
important naturally occurring radioactive isotope of potassium, K-40,
which decays by positron emission.  0.0117% of all the potassium atoms
in the world are this isotope (one out of every 8540 potassium atoms).
K-40 is used in the radioactive dating of igneous rocks.  See this
link for more details: http://id-archserve.ucsb.edu/Anth3/Courseware/Chronology/09_Potassium_Argon_Dating.html

It is true, however, that positron emission is rare in naturally
occurring radioactive isotopes.  A glance through the CRC Handbook of
Chemistry and Physics (77th edition) Table of the Isotopes reveals
that of the 18 naturally occurring radioactive nuclei with isotopic
abundances over 0.01%, only K-40 decays by positron emission; the
others decay by emitting alpha particles, beta particles (electrons),
or gamma rays, or by capturing electrons.

If you will allow me to rephrase your question, let's ask instead,
"Why is decay by positron emission such a rare process among naturally
occurring radioactive isotopes?"  There are three reasons.

In beta decay, or electron emission, a neutron is converted into
a proton, an electron, and an antineutrino.  Symbolically,

      0         +       -      _
     n   -->   p   +   e   +   v

This reaction can proceed inside or outside the nucleus of an atom,
even with free neutrons because the neutron on the left-hand side is
more massive than its decay products on the right-hand side, and the
excess mass is converted into the kinetic energies of the decay
products through Einstein's famous formula E=mc^2.

In positron emission, a proton is converted into a neutron, a positron
(or antielectron), and a neutrino.  Symbolically,

      +         0       +
     p   -->   n   +   e   +   v

This reaction can NOT proceed outside the nucleus because the proton
on the left-hand side is LESS massive than its decay products on the 
right-hand side.  Free protons are stable against this kind of decay.
In the nucleus, some of the energy that binds the protons and neutrons
together can be used to make the reaction go.

REASON #1: Electron emission is energetically favored over positron
           emission because neutrons are more massive than protons.

Most naturally occurring nuclides, especially the heavier isotopes,
contain more neutrons than protons.  The protons, being positively
charged, repel each other through the electric force but they also
attract each other through the strong force.  Neutrons, being neutral,
are not affected by the electric force, but do interact through the
strong force.  Neutrons supply the "glue" to bind a nucleus together.

Neutrons and protons are spin one-half particles (so are electrons)
and they obey the Pauli Exclusion Principle: No two spin one-half
particles can be in the same place at the same time.  Because the
neutrons and protons can not exist on top of one another, newly added
particles must go into higher and higher energy states.

In order for a nucleus to emit a positron, a proton in the nucleus
must convert to a neutron.  Since there are already a lot of neutrons
in the nucleus, it is not likely that the newly created neutron will
find an unfilled low-energy state.  On the other hand, in order for
a nucleus to emit an electron, a neutron must convert to a proton.
Since there are not as many protons in the nucleus, chances are good
that the newly created proton will find an unoccupied low-energy state.

REASON #2: There are more neutrons than protons in most nuclei.  The
           Pauli Exclusion Principle favors changing neutrons into
           protons by emitting electrons (beta decay) over changing
           protons into neutrons by positron emission.

There is a radioactive decay process called "electron capture" which
is always found whenever positron emission occurs.  In electron
capture, an electron orbiting around the nucleus of an atom sometimes
wanders into the nucleus and combines with a proton to produce a
neutron and a neutrino.  Symbolically,

      +       -         0
     p   +   e   -->   n   +   v

As in positron emission, this process can only take place inside the
nucleus because the left-hand side is less massive than the right-hand
side so some energy must be supplied by the nucleus itself to make the
reaction go.  But this reaction requires LESS energy from the nucleus
than positron emission requires.

In fact, there are two other naturally occurring radioactive isotopes
besides potassium-40 which decay by electron capture: vanadium-50 and
tellurium-123.  But neither of these isotopes can emit positrons
because the nuclei can not supply enough energy to run the reaction.
The energy needed is relatively large in the nuclear realm -- twice 
the rest mass energy of the electron, 1.022 MeV.

REASON #3: There is a hurdle or energy threshold to overcome before
           positron emission is possible.


--Dr. Randall J. Scalise    http://www.phys.psu.edu/~scalise/