1. Oct 5, 2006

### 3trQN

During radioactive decay, what determines if the emission of a beta particle will be positronic or electronic?

2. Oct 5, 2006

### Staff: Mentor

It depends on which of the two final nuclei has a smaller mass than the initial nucleus. The mass difference provides the energy for the electron and antineutrino (or positron and neutrino).

3. Oct 8, 2006

### Edgardo

For beta-minus decay the following condition must be fulfilled:
$$Q \approx [m_{at}(Z,A)-m_{at}(Z+1,A)]c^2 > 0$$

with
$$Q$$: Q-value
$$m_{at}(Z,A)$$: mass of the atom before beta-minus decay
$$m_{at}(Z+1,A)$$: mass of the atom after beta-minus decay

For beta-plus decay the following condition must be fulfilled:

$$Q \approx [m_{at}(Z,A)-m_{at}(Z-1,A)]c^2-1.022 \rm{MeV} > 0$$

with
$$Q$$: Q-value
$$m_{at}(Z,A)$$: mass of the atom before beta-plus decay
$$m_{at}(Z-1,A)$$: mass of the atom after beta-plus decay
$$1.022 \rm{MeV}$$: two times the electron (or positron) mass

Thus, for beta-plus decay the mass of the atom before decay
must be at least two electron masses greater than after the decay.

Last edited: Oct 8, 2006
4. Oct 8, 2006

### Astronuc

Staff Emeritus
The mass defect determines if a nuclei is radioactive, i.e. will decay spontaneously.

If one looks at a chart of the nuclides arranged with mass on the abscissa and nuclear charge (atomic number, Z) on the ordinate, then the positron emitters are above the stability line, while the beta emitters are below the stability line. The positron emitters have an excess of protons, while the beta emitters have an excess of neutrons, or conversely a deficiency of protons.

At a certain mass, the process (phenomenon) of electron capture (EC)becomes more likely than positron emission. In EC, an K-shell (1s) electron is 'captured' by the nucleus and a proton is transformed into a neutron. The effect is the same as positron emission - Z decreases by 1.