How do you balance a nuclear equation?

To balance a nuclear equation, ensure the sum of atomic numbers and mass numbers are equal on both sides.

Balancing a nuclear equation involves making sure that the total number of protons (atomic numbers) and the total number of nucleons (mass numbers) are the same before and after the reaction. This is similar to balancing chemical equations, but instead of atoms, we are dealing with subatomic particles.

First, identify the reactants and products in the nuclear reaction. For example, in the alpha decay of Uranium-238, the equation is written as:
\[ _{92}^{238}\text{U} \rightarrow _{2}^{4}\text{He} + _{90}^{234}\text{Th} \]

Here, Uranium-238 decays into Thorium-234 and an alpha particle (Helium-4 nucleus). To balance this equation, check the atomic numbers and mass numbers:
- The atomic number of Uranium (92) equals the sum of the atomic numbers of Thorium (90) and Helium (2).
- The mass number of Uranium (238) equals the sum of the mass numbers of Thorium (234) and Helium (4).

Next, if the equation involves beta decay, where a neutron turns into a proton and emits an electron (beta particle), the atomic number increases by one, but the mass number remains unchanged. For example:
\[ _{6}^{14}\text{C} \rightarrow _{7}^{14}\text{N} + _{-1}^{0}\text{e} \]

In this case, Carbon-14 decays into Nitrogen-14 and a beta particle. The atomic number of Carbon (6) increases to Nitrogen (7), and the mass number remains 14.

By ensuring the sums of atomic and mass numbers are equal on both sides of the equation, you can successfully balance any nuclear reaction. This principle helps us understand the conservation of mass and charge in nuclear processes.