#beta^-# decay problem?

In #beta^-# decay a neutron in a nucleus is transformed into a proton, an electron, and an antineutrino:

#n rarr p + e^(-) + barv #

(a) The physical quantity not conserved in #beta^-# decay is____

(b) The particle denoted by the question mark in the reaction

#N_7 ^(13)" rarr# #C _6 ^(13)" +e^(-) + ?#
is____.

Note that the superscript and subscript in #C _6 ^(13)"#, for instance, are respectively the mass number A and atomic number Z of the carbon nucleus.

1 Answer
Apr 17, 2018

As shown in the question, in #beta^-# decay, a neutron splits into a proton (which stays in the nucleus) and emits an electron and antineutrino:

#""_(0)^(1) n -> ""_(1)^(1) p + ""_(-1)^(0) e + barupsilon#

where #""_(0)^(1)n# is a neutron, #""_(1)^(1) p# is a proton, and #""_(-1)^(0)e# is an electron.

Part (a) shows that the atomic number is not conserved in #beta^-# decay, otherwise known as #beta# decay. Actually, it increases #Z# by #1# and keeps #A# the same.

In an explicit example, the question presents:

#""_(7)^(13) "N" -> ""_(6)^(13) "C" + ""_(-1)^(0) e + ?#

There may be a typo in the problem... clearly, #6 - 1 ne 7#. I think it should be...

#""_(6)^(13) "C" -> ""_(7)^(13) "N" + ""_(-1)^(0) e + ?#

In THAT case, it would be an antineutrino. It IS true that #7 - 1 = 6#...