$^{14}_7$N  + X → $^{14}_6$C  +  $^1_1$P In the reaction above, X is

Analyze the question: This is a nuclear reaction. We need to find the particle X that balances the equation. In nuclear equations, the sum of mass numbers (top) and the sum of atomic numbers (bottom) must be equal on both sides.

Concept: Conservation of mass number (A) and atomic number (Z):

• Total A on the left = total A on the right
• Total Z on the left = total Z on the right

Solution:

Reaction: ¹⁴₇N + X → ¹⁴₆C + ¹₁P (where ¹₁P is a proton, ¹₁H)

1. Mass number: 14 + A(X) = 14 + 1 A(X) = 15 − 14 = 1

2. Atomic number: 7 + Z(X) = 6 + 1 Z(X) = 7 − 7 = 0

So X has mass number 1 and charge 0, which is ¹₀n, a neutron.

Check against the options:

• A. Proton is ¹₁p, so Z = 1. Wrong.
• B. Alpha particle is ⁴₂He. Wrong.
• C. Beta particle is ⁰₋₁e. Wrong.
• D. Neutron is ¹₀n. Matches.

This is the real reaction that produces carbon-14 in the upper atmosphere: ¹⁴₇N + ¹₀n → ¹⁴₆C + ¹₁H. It is the basis of radiocarbon dating.

Exam tip: For missing particles, just do two quick subtractions: top numbers (mass) and bottom numbers (charge). Remember: mass 1 and charge 0 means neutron, mass 1 and charge 1 means proton, mass 0 and charge −1 means beta, and mass 4 and charge 2 means alpha.