Question

How to calculate maximum beta energy (0.634 MeV) of fluorine-18? I've tried using binding energy formula, but the result is different?!

Answer 1

Fluorine-18 decays to Oxygen-18 via positron emission as shown in the figure above. Referring to the part table above we calculate the energy available for the positron emission.

`E=180009380-17.99991610=0.001777\ am u` `=>E=0.001777xx931.5=1.6552755\ Mev`

When a positron is ejected from the parent nucleus, the daughter `(Z−1)` atom must also shed one of its orbital electron to balance charge. Therefore, mass of two electrons is ejected from the parent nucleus, (one of the emitted positron and the other of the orbital electron).

Mass of one electron `=0.511\ Mev`
`:.` Energy used in one positron `+` one electron`=2xx0.511=1.022\ Mev`

Now maximum positron energy`=1.655-1.022=0.633\ Mev`

Note: For energy difference between parent and daughter nuclei `<2m_ec^2` positron emission cannot occur.