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7.2.4Nuclear Physics

Decay Equations

5 min read 5 parts Lesson 9 of 19 1 quiz

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Section 1 of 5Balancing Rules

7.2.4 Decay Equations
Mass number
  • The total mass number (A) must be the same on both sides of a decay equation, because nucleons are conserved.
Atomic number
  • The total atomic number (Z) must be the same on both sides, so the total charge is conserved in the decay.
Alpha particle
  • Written as ⁴₂He or ⁴₂α, with a mass number of 4 and an atomic number of 2.
Beta particle
  • Written as ⁰₋₁e or ⁰₋₁β, with a mass number of 0 and an atomic number of −1.

Section 2 of 5Alpha Decay

1
An unstable parent nucleus emits an alpha particle, so its mass number falls by 4.
2
Its atomic number falls by 2 because two protons leave the nucleus with the alpha particle.
3
A new element is therefore formed, with a different atomic number from the parent nucleus.
4
Example: uranium-238 (²³⁸₉₂U) emits an alpha particle and becomes thorium-234 (²³⁴₉₀Th).

Section 3 of 5Beta Decay

1
A neutron in the parent nucleus changes into a proton and an electron.
2
The electron is emitted as a beta particle, so the mass number stays the same.
3
The proton stays in the nucleus, so the atomic number increases by one.
4
Example: carbon-14 (¹⁴₆C) decays to nitrogen-14 (¹⁴₇N) with a beta particle emitted.

Section 4 of 5Worked Example

Question

  • Radium-226 (atomic number 88) undergoes alpha decay.
  • Write the balanced decay equation and identify the daughter nucleus.

  1. Mass number of daughter = 226 − 4 = 222.
  2. Atomic number of daughter = 88 − 2 = 86, which is radon (Rn).
  3. Equation²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He, with mass numbers 226 = 222 + 4 and atomic numbers 88 = 86 + 2.

Answer ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He (daughter nucleus is radon-222)

Section 5 of 5Exam Checklist & Tips

7.2.4 – Key Points for the Exam

  • Parent nucleus The original unstable nucleus before a decay takes place.
  • Daughter nucleus The nucleus produced after a decay takes place.
  • Mass number The total number of protons and neutrons in a nucleus, shown as A.
  • Atomic number The number of protons in a nucleus, shown as Z.
  • Decay equation A balanced equation showing the particles before and after a radioactive decay.

Common Mistakes

  • Subtracting only the protons for alpha decay;
    • an alpha emission lowers the mass number by 4 and the atomic number by 2.
  • Forgetting that beta decay keeps the mass number the same while raising the atomic number by one.
  • Giving an electron a mass number of 1; an electron has a mass number of 0 and atomic number −1.
  • Writing the beta decay as if the proton leaves the nucleus; the proton stays in the nucleus.
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