Nuclear Equations

A nuclear equation shows what a nucleus becomes when it decays. Both the mass numbers and the atomic numbers must balance across the arrow, and checking that they do is the quickest way to catch an error.

Alpha decay — the nucleus loses 2 protons and 2 neutrons:

• Mass number decreases by 4
• Atomic number decreases by 2

²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He

Check: 234 + 4 = 238 ✓ and 90 + 2 = 92 ✓

The alpha particle may be written ⁴₂He or ⁴₂α.

Beta decay — a neutron turns into a proton, and the electron created is emitted:

• Mass number stays the same (a nucleon has changed type, but the count is unchanged)
• Atomic number increases by 1

¹⁴₆C → ¹⁴₇N + ⁰₋₁e

Check: 14 = 14 ✓ and 7 + (−1) = 6 ✓

The beta particle is written ⁰₋₁e or ⁰₋₁β. Its atomic number of −1 looks strange but is exactly what makes the equation balance, and leaving it out is the most common mistake here.

Gamma emission — a nucleus releases energy without changing its composition:

• Mass number unchanged
• Atomic number unchanged

So gamma emission alone never changes one element into another. Alpha and beta decay always do.

Summary:

Working out an unknown. If a question gives the parent and the daughter, compare the numbers. A drop of 4 in A and 2 in Z is alpha. No change in A with Z up by 1 is beta.

Example: ²²⁶₈₈Ra decays to ²²²₈₆Rn. The mass number has fallen by 4 and the atomic number by 2, so this is alpha decay, and the full equation is ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He.