Final answer:
The particle needed to complete the nuclear equation for the β+ decay of potassium-40 is Argon-40 (40Ar). During beta-plus decay, a proton in potassium-40 is converted into a neutron, resulting in a nucleus with one less proton, which is argon-40.
Step-by-step explanation:
The equation provided represents a nuclear process where a potassium-40 nucleus (40K) undergoes beta-plus decay (β+ decay) to form a new nucleus X and emits a positron (e+). In β+ decay, a proton in the nucleus is converted into a neutron and a positron is emitted.
The daughter nuclide will have one less proton than the parent nuclide. The correct particle or nucleus X needed to complete the equation 40K → e+ + (X) is 40Ar (Argon-40), since potassium (K) has an atomic number of 19 and Argon (Ar) has an atomic number of 18, one less than potassium.
The full nuclear equation for the beta-plus decay of 40K is:
4019K → 4018Ar + 0+1e (positron)