What is beta decay?

See this to start with.

http://socratic.org/questions/how-do-i-figure-out-nuclear-equations-involving-radioactive-decay#218098

Different modes of beta decay are as follows. There is no change of mass number of the daughter nucleus. However the atomic number changes to one greater in case of #beta^-# electron and changes to one less in case of #beta^+# positron decay.

$ Electron emission, #beta^-# decay. Here the nucleus emits an electron and an electron antineutrino #bar nu_e#. Example neutron changing into a proton.

#""_0^1n -> ""_1^1p + ""^0e^− + bar nu_e#

#""_55^137Cs -> ""_56^137Ba + ""^0e^− + bar nu_e#

Positron emission, #beta^+# decay. Here the nucleus emits a positron and an electron neutrino #nu#. Consider decay of a proton in the nucleus.

#""_1^1p->""_0^1n+ ""^0e^+ +nu_e#

#""_11^22Na ->""_10^22Ne +""^0e^++ nu_e#

Electron capture, In this case the nucleus captures an orbiting electron and emits a neutrino. The daughter nucleus is unstable. Daughter nucleus has atomic number one less.

#""_11^22Na + ""^0e^− ->""_10^22Ne + nu_e#

-.-.-.-.-.-.-.-.-.-.-.-.-.-..-.-.-.-..-.-.-

@ For sake of completeness. Following types of #beta# decay are also included.

Bound state beta decay, In this decay free neutron or nucleus beta decays to electron and antineutrino. The electron thus produced is not emitted but is captured by the atom to fill up one of its vacant electronic shells, the daughter nucleus is unstable.

Double beta decay, Similar to single electron case but some nucleus emits two electrons and two antineutrinos. Daughter nucleus has atomic number two more.

Double electron capture, some nucleus absorbs two orbital electrons and emits two neutrinos. The daughter nucleus is unstable and has atomic number two less.

Electron capture with positron emission, the nucleus absorbs one orbital electron, emits one positron and two neutrinos. Daughter nucleus has atomic number two less.

Double positron emission, A nucleus emits two positrons and two neutrinos. Daughter nucleus has atomic number two less.