Final answer:
The nuclear equations for alpha decay, beta decay, electron capture, and positron emission are as follows: AZ → A-4Z-2 + 42He, AZ → AZ+1 + 0-1e, AZ + 0-1e → AZ-1, and AZ → AZ-1 + 01e, respectively.
Step-by-step explanation:
The nuclear equation for alpha decay is represented as AZ → A-4Z-2 + 42He. For example, the alpha decay of 19885At is written as 19885At → 19483Bi + 42He. This means that an alpha particle, which is a helium nucleus, is emitted from the nucleus of the parent isotope.
The nuclear equation for beta decay is represented as AZ → AZ+1 + 0-1e. For example, the beta decay of 3516S is written as 3516S → 3517Cl + 0-1e. This means that a neutron in the nucleus of the parent isotope is converted into a proton, and an electron is emitted from the nucleus.
The nuclear equation for electron capture is represented as AZ + 0-1e → AZ-1. For example, the electron capture of 20180Hg is written as 20180Hg + 0-1e → 20179Au. This means that an electron from an electron shell is captured by the nucleus, combining with a proton to form a neutron.
The nuclear equation for positron emission is represented as AZ → AZ-1 + 01e. For example, the positron emission of 16C is written as 16C → 15N + 01e. This means that a proton in the nucleus of the parent isotope is converted into a neutron, and a positron is emitted from the nucleus.