Nuclear Accounting

When writing nuclear equations, there are some general rules that will help you:

• The sum of the mass numbers (top numbers) on the reactant side equal the sum of the mass numbers on the product side.
• The atomic numbers (bottom numbers) on the two sides of the reaction will also be equal.

In the alpha decay of U²³⁸ , both atomic and mass numbers are conserved:

• mass number: 238=4+234

• atomic number: 92=2+90

Confirm that this equation is correctly balanced by adding up the reactants' and products' atomic and mass numbers. Also, note that because this was an alpha reaction, one of the products is the alpha particle, He24.

Note that both the mass numbers and the atomic numbers add up properly for the beta decay of Thorium-234   :

• mass number: 234=0+234

• atomic number: 90=−1+91

The mass numbers of the original nucleus and the new nucleus are the same because a neutron has been lost, but a proton has been gained and so the sum of protons plus neutrons remains the same. The atomic number in the process has been increased by one since the new nucleus has one more proton than the original nucleus. In this beta decay, a thorium-234 nucleus has one more proton than the original nucleus. In this beta decay, a thorium-234 nucleus has become a protactinium-234 nucleus. Protactinium-234 is also a beta emitter and produces uranium-234.

Once again, the atomic number increases by one and the mass number remains the same; confirm that the equation is correctly balanced.

Example 1

Complete the following nuclear reaction by filling in the missing particle.

Solution

This reaction is an alpha decay. We can solve this problem one of two ways:

Solution 1: When an atom gives off an alpha particle, its atomic number drops by 2 and its mass number drops by 4 leaving: Po84206

. We know the symbol is Po

, for polonium, because this is the element with 84 protons on the periodic table.

Solution 2: Remember that the mass numbers on each side must total up to the same amount. The same is true of the atomic numbers.

• Mass numbers: 210=4+?

• Atomic numbers: 86=2+?

We are left with  ₈₄ Po²⁰⁶