The three types of beta emission are;

  • Beta-minus (\beta^{-} ) decay
  • Beta-plus (\beta^{-} ) decay – otherwise known as positron emission
  • Orbital electron capture

\beta^{-} and \beta^{+} emission are discussed here. Orbital electron capture is a process that can occur when the ratio of neutrons to protons is low.

In this process, instead of a proton being converted into a neutron with the emission of a positron (and electron-neutrino), a proton rich nucleus of an electrically neutral atom absorbs an electron from one of the inner electron shells (or energy levels). This process there converts a proton into a neutron;

^{0}_{-1}e + \ ^{1}_{1}p \ \ \rightarrow \ \ ^{1}_{0}n

As shown on the page focusing on \beta^{-} and \beta^{+} , nuclear equations need to ensure charge, baryon number and lepton number are conserved, so first lets write a quark equation;

^{0}_{-1}e + \ ^{1}_{1}p \ \ \rightarrow \ \ ^{1}_{0}n
^{0}_{-1}e + uud \ \ \rightarrow \ \ ^udd
^{0}_{-1}e + u \ \ \rightarrow \ \ d

Charge:

^{0}_{-1}e + u \ \ \rightarrow \ \ d
-1 + \frac{2}{3} \ \ \rightarrow \ \ -\frac{1}{3}
-\frac{1}{3} \ \ \rightarrow \ \ -\frac{1}{3}

Charge is conserved. ✓

Baryon number:

^{0}_{-1}e + u \ \ \rightarrow \ \ d
0 + \frac{1}{3} \ \ \rightarrow \ \ \frac{1}{3}
\frac{1}{3} \ \ \rightarrow \ \ \frac{1}{3}

Baryon number is conserved. ✓

Lepton number:

^{0}_{-1}e + u \ \ \rightarrow \ \ d
+1 + 0 \ \ \rightarrow \ \ + 0
+1  \ \ \rightarrow \ \ 0

Lepton number is not conserved. ✓

So an additional particle must be emitted that does not affect the charge or the baryon number but does change the lepton number. What particle has no charge, no baryon number and a lepton number of -1?

Answer:

It must be a lepton and for no charge to be present the particle must be one of neutrinos – an antielectron-neutrino.

And so, the full quark transformation for orbital electron capture must be:

^{0}_{-1}e + u \ \ \rightarrow \ \ d + \ \bar{\nu{e}} 

Quantities conserved:

  • Charge: ✓
  • Baryon number: ✓
  • Lepton number: ✓

In addition to this the full process in which a proton transforms into a neutron is:

^{0}_{-1}e + \ ^{1}_{1}p \ \ \rightarrow \ \ ^{1}_{0}n + \ \bar{\nu_{e}}

For more information watch this YouTube clip: