Decay equations and half-life

Last time

Before we start: last time, in Half-life, uses of isotopes, fission and fusion, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.

A clock inside every nucleus

Archaeologists date a wooden spear by measuring how much radioactive carbon is left in it. Doctors choose an isotope that is gone from a patient's body in a day. Both rely on one fact: the number of radioactive nuclei in a sample falls by half in a fixed time, called the half-life. Before that, we need to see what happens inside the nucleus when it decays.

Alpha decay

When a nucleus emits an alpha particle, it loses 2 protons and 2 neutrons. The nucleon number falls by 4, and the proton number falls by 2. The element changes. Uranium-238 gives thorium-234 plus an alpha particle.

Beta decay

In beta decay, a neutron in the nucleus changes into a proton and an electron. The electron is emitted as the beta particle. The nucleon number is unchanged, and the proton number goes up by 1. The element changes. Carbon-14 gives nitrogen-14 plus a beta particle.

Gamma emission

A gamma ray carries away excess energy from the nucleus. It is often emitted just after an alpha or beta decay. The nucleon number and the proton number do not change. So gamma emission does not make a new element.

Balancing the equation

The top numbers, the nucleon numbers, must add up to the same total on both sides. The bottom numbers, the proton numbers or charges, must also add up to the same total. Check uranium: 238 equals 234 plus 4. And 92 equals 90 plus 2.