Question

What do the quark compositions and other quantum numbers imply about the relationships between the Δ+ and the proton? The Δ0 and the neutron?

a) Δ+ and proton have different quark compositions; Δ0 and neutron have identical quark compositions
b) Δ+ and proton have identical quark compositions; Δ0 and neutron have different quark compositions
c) Δ+ and proton have identical quark compositions; Δ0 and neutron have similar quark compositions
d) Δ+ and proton have different quark compositions; Δ0 and neutron have similar quark compositions

Answer 1

The Δ+ has the same quark composition as the proton but has a different spin and mass, and the same applies to the Δ⁰ relative to the neutron.

Step-by-step explanation:

The quark compositions and other quantum numbers reveal significant differences in the relationships between the Δ+ and the proton as well as the Δ⁰ and the neutron. The Δ+ and the proton are both composed of uud quarks, but the Δ+ has a higher total spin quantum number of 3/2 compared to the proton’s spin of 1/2.

Conversely, the Δ⁰ is also composed of udd quarks, similar to the neutron, but it also has a spin of 3/2, which differentiates it from the neutron with a spin of 1/2. The quantum numbers for these particles suggest that although the quark compositions are identical, the properties of the particles such as their spin and mass energy are different due to the particles’ differing spins and the energy associated with them.

Specifically, the mass of the Δ+ with spin 3/2 is about 1.3 times the mass of the proton, and the Δ⁰ baryon with spin 3/2 is about 1.3 times the mass of the neutron.