Question

What do the quark compositions and other quantum numbers imply about the relationships between the \[{{\rm{\Delta }}^{\rm{ + }}}\]and the proton? The \[{{\rm{\Delta }}^{\rm{0}}}\]and the neutron?

Short answer

The \[{{\rm{\Delta }}^{\rm{ + }}}\] and \[{{\rm{\Delta }}^{\rm{0}}}\] are the higher end mass excitation of proton and neutron respectively.

Step-by-step solution

Definition of Concept

Protons and neutrons are called fermions due to their half-integral spin. The composition of protons is uud whereas that of the neutron is udd, where u is the up quark and d is the down quark.

Step 2:Explain the implications about the relationships between the (\[{{\rm{\Delta }}^{\rm{ + }}}\]and the proton) and (the \[{{\rm{\Delta }}^{\rm{0}}}\]and the neutron)

The\[{{\rm{\Delta }}^{\rm{ + }}}\]and\[{{\rm{\Delta }}^{\rm{0}}}\]represent the higher-end mass excitations of the proton and neutron, respectively\[{{\rm{\Delta }}^{\rm{ + }}}\]and\[{{\rm{\Delta }}^{\rm{0}}}\]have a composition (uud) and (udd) respectively.Here u and d are up and down quarks respectively. The charge on\[{{\rm{\Delta }}^{\rm{ + }}}\]and\[{{\rm{\Delta }}^{\rm{0}}}\]is +e and zero respectively, with spin and isospin of\[{\rm{3/2}}\], whereas proton has +e charge and neutronis neutral, with spin and isospin of\[{\rm{1/2}}\].

Therefore, the \[{{\rm{\Delta }}^{\rm{ + }}}\]and \[{{\rm{\Delta }}^{\rm{0}}}\]are said to be the higher-end mass excitations of the proton and neutron, respectively.