What Is Beta Decay?

                                                           
Definition: In nuclear Physics, Beta Deacay is the type of radioactive decay, in which an atomic nucleus spontaneously decays into another atomic nucleus to become more stable by emitting an electron ( e− or β− ) or positron ( e+ or β+ ).

In β− decay:

In this subtype of beta decay, no. of neutrons are more than the no. of protons then a neutron turns into proton and makes a new electron e− this electron is not an ordinary electron, 
its a very fast moving electron, And this fast moving electron is Beta Particle. 

Atomic number Z of daughter nucleus is increased by 1, 
while its mass number A remain unchanged,
which is shown as:

                                                                    n → p + e− 

In β−  decay, β− decay generally occurs in neutron-rich nuclei, the weak interaction converts an atomic nucleus into a nucleus with one higher atomic number while emitting an electron (e− ):

A
ZX → A
Z+1Y + e− 

14
6C   → 14
7N + e− 

where A and Z are the mass number and atomic number of the decaying nucleus.

In β+ decay:

In this subtype of beta decay, no. of protons are more than the no. of neutrons, and a proton turns into neutron and makes a new positron e+,this positron is not an ordinary positron, its a very fast moving positron,
And this fast moving positron is Beta Particle. 
Atomic number Z of daughter nucleus is decreased by 1, while its mass number A remain unchanged. In this beta decay, a proton turns into neutron and positron e+ , which is shown as: 

                                                                     p → n + e+ 

In β+ decay, or "positron emission", the weak interaction converts a nucleus into its next-lower neighbor on the periodic table while emitting a positron (e+):

A
ZX → A
Z−1Y + e+  

23 12Mg

→

22 11Na

+

e+

where A and Z are the mass number and atomic number of the decaying nucleus.

When beta decay occurs:

1) when neutrons to protons ratio is above the Band of stability, then  β−  decay occurs.

 As

12

6C → neutron/proton = 6/6 = 1/1 → Its pretty good ratio for stable nuclei which don't go under decay.

14
6C → n/p = 8/6 = 1.33 →Its ratio is big high and nuclei will go under decay.

                                                                      n → p + e− 

Result will be 

14
6C → 14
7N + e−

2) when neutrons to protons ratio is below the Band of stability, then  β+  decay occurs.

As

23

12Mg → neutron/proton = 11/12 = 0.9116 → Its not good ratio and nuclei will go under decay. 

                                                     p → n + e+  

Result will be

23
12Mg → 23
11Na + e+

 

The Electron K.E in the beta decay are found to vary contineously from zero to maximum value as shown by graph. As only 1/3 of max. energy is taken by electron and 2/3 of max. energy seems to be missed.

And we know that law of conservation of energy must hold

in beta decay. This problem was solved by Fermi, who

gave neutrino hypothesis, first suggested by Pauli.

According to this hypothesis, an additional partical

called neutrino ( v ) or antineutrino ( ν ) also created in

beta decaywhich carries away the missing energy. Neutrino has very small mass ( of the order of few ev ) and has charge zero.This hypothesis was confirmed by experiments later.

hence, both energy and momentum ( linear, angular ) are conserved in this decay process. 

On the basis of neutrino hypothesis beta decay process can be written as:

For  β−                                     

                             n → p + e− +  ν

                                                                       14
6C → 14
7N + e− + ν
e

For β+ 

                    p → n + e+ +  v

                                                        23
12Mg → 23
11Na + e+ + v

                                                                                                  10
6C → 10
5B + e+ + v
  

Electron capture (K-capture):

A beta decay occur in which an electron is captured from inner orbits by nucleus, with the result that proton becomes a neutron and a neutrino is emitted as shown:

                                                        p  + e− →  n + v

e.g.

                                   

                                                                          1¹H+ e− →  n + v
The emitted neutrino is mono-energetic. This decay is also called K-capture because the innermost electron of an atom belongs to the K-shell of the electronic configuration of the atom, and this has the highest probability to interact with the nucleus.