(positron)
emission from a nucleus, there is another competing process known as electron
capture (electron from an inner orbit, say, the K- shell, is captured by the
nucleus and a neutrino is emitted).
Show that if emission
is energetically allowed, electron capture is necessarily allowed but not
vice-versa.
Answer:
For the positron emission, we
have
?(1)
And for
Electron Capture, we have
?(2)
If 
represents
the nuclear mass and in represents the atomic mass, then for 
as
the mass of 
or 
we have
Nuclear mass
of
Nuclear mass
of 
?(3)
Also
?(4)
From eqns.
(3) and (4), we find that if 
is necessarily greater
than zero.
However, if 
does
not always mean that 
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