can you tell me how the beta-plus decay process may be understood (i) at the level of individual nucleons and (ii) at the level of quarks, by writing a decay reaction in each case.
See above.
At the level of individual nucleons, a neutron is converted into a proton plus a beta particle (high energy electron) and an electron antineutrino.
A proton consists of 2 up and 1 down quark and a neutron consists of 1 up and 2 down quarks.
Sure! I can help you understand the beta-plus decay process at both the level of individual nucleons and at the level of quarks.
(i) At the level of individual nucleons:
Beta-plus decay occurs when a proton within the nucleus transforms into a neutron. This process is mediated by the weak nuclear force. In a beta-plus decay reaction, a proton emits a positron (e+) and a neutrino (νe), while simultaneously undergoing a conversion into a neutron. The decay reaction can be written as follows:
Source nucleus: A(Z, N)
↓ beta-plus decay
Daughter nucleus: A(Z-1, N+1) + e+ + νe
Here, A represents the atomic mass number, Z represents the atomic number (number of protons), and N represents the number of neutrons.
(ii) At the level of quarks:
Inside the nucleon, protons and neutrons are composed of quarks. A proton consists of two up quarks (u) and one down quark (d), while a neutron consists of two down quarks and one up quark. In beta-plus decay, a single up quark within a proton undergoes a transformation into a down quark. This is achieved through the exchange of a charged weak boson (W+). The decay reaction can be represented as follows:
Source quark content: uud
↓ beta-plus decay
Daughter quark content: udd + e+ + νe
In this representation, u denotes an up quark, d denotes a down quark, and e+ represents a positron. The neutrino (νe) is also emitted, but since it does not have a quark content, it is not explicitly mentioned.
It's important to note that electric charge is conserved in beta-plus decay, as the positron carries away the positive charge that is lost when the proton transforms into a neutron. Additionally, the conservation of lepton number is maintained, as the total number of leptons (positron and neutrino) remains the same before and after the decay.
I hope this explanation helps you understand beta-plus decay at both the nucleon and quark level!