7.7-7.9 - Nuclear equations and detectors

Nuclear notation

A nucleus can be written with two numbers next to its chemical symbol:

The top number, $A$, is the mass number. It counts the total number of protons and neutrons in the nucleus. The bottom number, $Z$, is the atomic number or proton number. It counts the number of protons, so it also identifies the element.

For example, $^{14}_{6}\text{C}$ is a carbon nucleus with mass number 14 and atomic number 6. It has 6 protons. Since the mass number counts protons plus neutrons, it has $14 - 6 = 8$ neutrons.

In a nuclear equation, the top numbers must balance and the bottom numbers must balance. This is often described as balancing mass and charge. For nuclei, the bottom number is the atomic number; for emitted particles such as beta-minus radiation, the bottom number is a charge number.

How emissions change the numbers

Each emitted radiation has its own mass number and charge number. The parent nucleus loses what is emitted, so the daughter nucleus has different $A$ and $Z$ values if particles with mass or charge leave.

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Alpha emission reduces both numbers because an alpha particle contains two protons and two neutrons. In beta-minus emission a neutron changes into a proton and an electron is emitted. This creates the electron; it was not an orbital electron escaping the atom. The beta-minus particle has mass number 0 and charge number $-1$, so the daughter nucleus must have atomic number one higher for the bottom numbers to balance. Gamma emission is electromagnetic radiation from the nucleus, so no protons or neutrons are lost. Neutron emission removes one neutron but no protons.

The word "beta" in this Edexcel point means beta-minus radiation. Do not use positron emission rules unless a question explicitly says beta-plus or positron.

Balancing nuclear equations

To balance a nuclear equation, compare the totals on each side.

First add the top numbers. The total mass number on the left must equal the total mass number on the right. Then add the bottom numbers. The total atomic number or charge number on the left must equal the total on the right.

For alpha emission from radium-226:

The mass numbers balance:

The bottom numbers balance:

For beta-minus emission, the negative bottom number is the common trap. Suppose thorium-234 emits beta-minus radiation:

The mass number stays 234 because the emitted beta-minus particle has mass number 0. The bottom numbers balance because $91 + (-1) = 90$. That is why beta-minus emission increases the daughter nucleus atomic number by 1.