Use given data to balance nuclear equations in terms of mass and charge

The idea

A nuclear equation must balance in two ways: the total mass number (nucleon number) on each side must be equal, and the total charge, given by the sum of proton numbers or ionic charges, must be equal. To balance an equation, add up the mass numbers of the reactants and set them equal to the sum for the products, then repeat for the atomic or charge values. For example, in alpha decay of radium-226, the equation ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He balances because 226 = 222 + 4 and 88 = 86 + 2. For beta decay, a neutron becomes a proton and an electron, so the mass number is unchanged while the charge rises by one on the nucleus. Use the supplied data rather than memorised values.

What earns the marks

• Balances the mass numbers so the totals on each side are equal.
• Balances the charge or proton numbers so the totals on each side are equal.
• Applies the given data rather than recalled values to find the unknown.
• Identifies the emitted particle from its mass number and charge.

Common mistakes and how to put them right

• Balances only the mass number and ignores charge.

  Put it right by checking both totals.

• Uses recalled values instead of the data supplied in the question.

  Put it right by reading the given figures.

• Treats an alpha particle as having charge 1⁻.

  Put it right by using the charge 2⁺ and mass number 4.

Exam tips

• Write the mass-number sum and the charge sum separately before choosing an option.
• Check each candidate option against both the mass balance and the charge balance.
• Use the data printed in the question rather than values you remember.