Final answer:
The missing particle in the nuclear equation is a beta particle (electron), indicated by the transformation of thorium to actinium, with the atomic number decreasing by one.
Step-by-step explanation:
The missing particle in the nuclear equation 231/90 Th → ______ 231/89 Ac can be determined by applying the conservation of mass and atomic numbers, meaning the sums on both sides of the nuclear equation must be equal. The thorium (Th) isotope undergoes decay, transforming into an actinium (Ac) isotope, with the atomic number decreasing by one. This indicates that a beta particle (an electron) has been emitted. Therefore, we can complete the nuclear equation as 231/90 Th → ⁰⁻¹e + 231/89 Ac, signifying the emission of a beta particle.