Final answer:
Electron capture conserves charge, electron family number, and total number of nucleons. Charge is balanced by the conversion of a proton into a neutron and the loss of an electron. Electron family number and total nucleons remain unchanged because the neutrino carries the family number and the nucleon count is constant.
Step-by-step explanation:
The question involves verifying the conservation laws in a nuclear reaction known as electron capture. In this process, an electron (e−) is captured by a proton in the nucleus, converting the proton into a neutron and emitting an electron neutrino (ve). The nuclear equation is written as AZXN + e− → AZ−1YN+1 + ve.
Before electron capture, the total charge would be +Z (from the nucleus) since a proton has a charge of +1. Post-capture, the charge is +Z−1, as one proton has converted into a neutron (no charge), and the electron is gone. Therefore, the total charge is conserved as the change is balanced by the disappearance of the electron.
The electron family number remains conserved because the initial electron (e−) and the emitted electron neutrino (ve) are both members of the electron family. Electron family number before the capture would be −1 (electron) but after the capture, there is +1 attributed to the emitted neutrino. The net change is zero, confirming the conservation of electron family number.
The total number of nucleons (protons and neutrons) also remains unchanged in this reaction. Initially, there are A nucleons, and after capture, the nucleus still contains A nucleons. Since A is the sum of protons and neutrons, the conversion from a proton to a neutron does not affect this total.