Answer :
The balanced nuclear equation for the beta decay of europium-157 is:
157/63Eu -> 157/64Gd + 0/-1e
In this equation, europium-157 (157/63Eu) undergoes beta decay, emitting a beta particle (0/-1e) and transforming into gadolinium-157 (157/64Gd). The beta particle represents an electron (e-) that is emitted from the nucleus during the decay process. The atomic numbers and mass numbers are conserved in the equation, indicating that the total number of protons and neutrons on both sides remains the same. The decay of europium-157 through beta decay results in the formation of gadolinium-157.
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