Question

The quark flavor changed \[ \to {\rm{u}}\] takes place in \[{\rm{\beta - }}\]decay. Does this mean that the reverse quark flavor changed \[{\rm{u}} \to \] takes place in \[{\rm{\beta + }}\] decay? Justify your response by writing the decay in terms of the quark constituents, noting that it looks as if a proton is converted into a neutron in \[{\rm{\beta + }}\]decay.

Short answer

Yes, \[u \to d\] flavor change occurs in \[{{\rm{\beta }}^{\rm{ + }}}\]decay.

Step-by-step solution

Concept Introduction

Quarks are divided into six flavors: up, down, charm, weird, top, and bottom. The masses of up and down quarks are the smallest of all quarks.

Explanation

Here\[{{\rm{\beta }}^{\rm{ - }}}\]decay is

\[(ud)d \to (ud)u + {e^ - } + {\bar \nu _e}\]

I,\[{{\rm{\beta }}^{\rm{ - }}}\]decay is where we spelled out the neutron and proton in terms of their quark components.

Where, we wrote out the neutron and proton in terms of their quark constituents, i.e. \[{\rm{n = udd and }}{{\rm{p}}^{\rm{ + }}}{\rm{ = udu}}\]. On the other hand, \[{{\rm{\beta }}^{\rm{ + }}}\]decay is given with\[(ud)u \to (ud)d + {e^ + } + {\nu _e}\]

A proton \[{{\rm{p}}^{\rm{ + }}}{\rm{ = udu}}\]has been transformed into a neutrino \[{{\rm{p}}^{\rm{ + }}}{\rm{ = udu}}\]. This reaction may be generated from (1) by moving particles from the right to the left side and "crossing to the opposite side." Because particles transform into their antiparticles in this operation, our electron \[{{\rm{e}}^{\rm{ - }}}\]became a positron \[{{\rm{e}}^{\rm{ + }}}\]and our electron antineutrino \[{{\rm{\bar \nu }}_{\rm{e}}}\]became a neutrino \[{{\rm{\nu }}_{\rm{e}}}\]. In most cases, a response can occur in both directions. We infer that in \[{{\rm{\beta }}^{\rm{ + }}}\]decay, the reverse flavor change happens.