The radioactive decay of uranium-238 (U-238) by alpha emission can be represented with the following balanced nuclear chemical equation:
\[ ^{238}{92}\text{U} \rightarrow ^{234}{90}\text{Th} + ^{4}_{2}\text{He} \]
In this equation, uranium-238 decays into thorium-234 (Th-234) and an alpha particle (which is the same as a helium-4 nucleus, He-4). The atomic and mass numbers on both sides of the equation are balanced.