How does beta decay change the nucleus?
Beta decay causes a neutron to become converted to a proton.
When C-14 undergoes beta decay it changes into N-14, the addition of a proton changes the identity of the atom.
C-14 has 6 protons and 8 neutrons
N-14 has 7 protons and 7 neutrons
(notice that the N-14 has added a proton and lost a neutron)
We can better understand this process by knowing about quarks.
A proton has two up quarks and a down quark. uud
A neutron has one up quark and two down quarks. udd
So beta decay causes a down quark to become converted into an up quark. The reason why protons and neutrons have a tiny difference in their masses is because of a slight difference in the mass of up and down quarks.