Nuclear Equation Calculator

Balance nuclear equations by conserving mass number and atomic number. Identify unknown nuclides in alpha decay, beta decay, positron emission, and electron capture reactions.

☢️ Nuclear Chemistry📐 A and Z conserved in nuclear reactions🧪 Chemistry
Parent mass number A
Parent atomic number Z
Decay type
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
Nuclear Equation Calculator—A and Z conserved in nuclear reactionsnuclide

Step-by-Step Examples

Example 1
U-238 Alpha Decay

U-238 (A=238, Z=92) undergoes alpha decay.

  • Alpha: loses He-4, so A-4=234, Z-2=90
  • Z=90 is Thorium (Th)
  • 238U to 234Th + 4He
✓ Product: Th-234 (thorium-234)
Example 2
C-14 Beta Decay

C-14 (A=14, Z=6) undergoes beta minus decay.

  • Beta-: A stays 14, Z increases by 1 to 7
  • Z=7 is Nitrogen (N)
  • 14C to 14N + e^- + antineutrino
✓ Product: N-14
Example 3
F-18 Positron Emission

F-18 (A=18, Z=9) undergoes beta+ emission.

  • Beta+: A stays 18, Z decreases by 1 to 8
  • Z=8 is Oxygen (O)
  • 18F to 18O + e^+ + neutrino
✓ Product: O-18

Real-World Applications

🏥
PET Scanning
F-18 positron emission used in PET scans. Gamma photons from e+/e- annihilation detected.
☢️
Radiation Safety
Knowing decay type and daughter nuclide determines radiation hazard and required shielding.
🌍
Geochemistry
Radiometric dating uses decay chains: U-238 to Pb-206 through 14 steps.
🧪
Nuclear Medicine
Tc-99m from Mo-99 decay: isomeric transition (gamma). Most used nuclear medicine isotope.

Common Mistakes to Avoid

⚠️
Mass number A is conserved

Total A of products = A of reactant. Alpha: A decreases by 4. Beta: A unchanged. Positron: A unchanged.

⚠️
Atomic number Z is conserved

Total Z of all particles = Z of parent. Alpha: Z decreases by 2. Beta-: Z increases by 1. Beta+: Z decreases by 1.

⚠️
Neutrinos are emitted in beta decay

Beta decay also produces electron neutrino (beta-) or electron antineutrino (beta+). They carry some energy but have negligible mass and do not affect A or Z.

Frequently Asked Questions

What are the main types of radioactive decay? ▾
Alpha (emit He-4), Beta minus (neutron to proton), Beta plus (proton to neutron), Gamma (energy release, no A or Z change), Electron capture (proton captures e^-).
What is alpha decay? ▾
Emission of He-4 nucleus (2 protons + 2 neutrons). Typical for heavy nuclides (Z > 82). Example: Ra-226 to Rn-222 + He-4.
What is beta decay? ▾
Beta-: neutron to proton + electron + antineutrino. Beta+: proton to neutron + positron + neutrino. Used in medical imaging (PET).
What is gamma emission? ▾
High-energy photon released when nucleus drops from excited to ground state. Same A and Z. Often follows alpha or beta decay. Example: Co-60 medical/industrial source.
What is the decay chain of uranium? ▾
U-238 undergoes 14 sequential decays to reach stable Pb-206. Chain includes Ra-226 (radium), Rn-222 (radon), and several short-lived isotopes.

Related Chemistry Calculators

☢️ Radioactive Decay☢️ Nuclear Symbol☢️ Isotope Abundance⏱️ Half-Life⚗️ Atomic Mass Isotopes

Formula Explorer connections

Interpretation: This relationship connects isotopic composition, decay, radiation, mass defect or nuclear energy to a measurable quantity. Assumption: Use the correct nuclide, decay constant, branching behavior and time units. Radiation estimates also depend on geometry, shielding and detector response.

Nuclear Q-Value Calculator →Nuclear Symbol Calculator →Radiation Dose Rate Calculator →Chemistry Formula Explorer →