Final answer:
In the alpha decay of Carbon-13, the nucleus emits an alpha particle resulting in a Beryllium-9 daughter isotope. The equation will be

Step-by-step explanation:
The balanced nuclear equation for the alpha decay of Carbon-13 is as follows:

In this reaction, a Carbon-13 nucleus emits an alpha particle (alpha decay), resulting in the formation of a Beryllium-9 (daughter isotope) and an alpha particle, which is a Helium-4 nucleus. It is important to ensure that the mass and atomic numbers are conserved in this nuclear equation.
The mass number decreases by four, and the atomic number decreases by two, reflecting the loss of two protons and two neutrons that make up the alpha particle.