Aluminum-27 is bombarded with an alpha particle, producing phosphorus-30 and one additional particle. Write the balanced nuclear equation for this artificial transmutation, identifying the missing particle by conserving both mass number and atomic number.

Setting up the equation: ²⁷₁₃Al + ⁴₂He → ³⁰₁₅P + (missing particle). Mass number balance: 27 + 4 = 30 + (missing particle's mass number), so the missing particle has mass number 1. Atomic number balance: 13 + 2 = 15 + (missing particle's atomic number), so the missing particle has atomic number 0. A particle with mass number 1 and atomic number 0 is a neutron (¹₀n). The full balanced equation is ²⁷₁₃Al + ⁴₂He → ³⁰₁₅P + ¹₀n. Identifying the missing particle as a proton (¹₁H) incorrectly assigns it atomic number 1 instead of the correctly balanced value of 0. Identifying it as a beta particle (⁰₋₁e) gives it the wrong mass number (0 instead of 1) and the wrong atomic number (−1 instead of 0), failing to balance the equation on either count. Identifying it as an alpha particle (⁴₂He) ignores that an alpha particle was already consumed as a REACTANT in this equation, and using another one as a product would fail both the mass number and atomic number balance entirely.