Radioactive decay.

Step 1 of 8

Unstable nuclei

In the exponents and logarithms Unit we saw that half the sample is left after every half-life. Here we ask what happens inside the nucleus itself. Some nuclei are not stable: they have too many neutrons, too few, or simply too many particles. At some moment a nucleus like that gives off radiation and becomes another nucleus, the daughter.

There are three common kinds of radiation, and in the Scene you choose between them with Radiation. The orange nuclei have not decayed yet, and the blue ones are daughters. Alpha is chosen now: notice that the daughters are smaller than the nuclei that decayed.

Step 2 of 8

Alpha decay

An alpha particle is a helium nucleus, $^{4}_{2}\mathrm{He}$⁠: two protons and two neutrons bound together. A nucleus that gives one off loses four particles, so the daughter is smaller. Every decay keeps both the number of protons and neutrons together and the charge. So in a nuclear equation the mass numbers add up to the same total on both sides, and so do the atomic numbers. For example, radium-226 decays to radon:

$^{226}_{88}\mathrm{Ra} \to {}^{222}_{86}\mathrm{Rn} + {}^{4}_{2}\mathrm{He}$$^{226}_{88}\mathrm{Ra} \to$${}^{222}_{86}\mathrm{Rn} + {}^{4}_{2}\mathrm{He}$⁠

The mass number fell by $4$⁠ and the atomic number by $2$⁠: the radium has become another element.

Step 3 of 8

Beta decay

In beta decay a neutron inside the nucleus turns into a proton, and an electron is made and shot out (with it leaves a tiny uncharged particle, an antineutrino). That electron comes from the nucleus, not from the shells. The number of particles in the nucleus has not changed, so the mass number stays the same, but there is one more proton. Here Radiation is Beta: the daughters no longer shrink.

The electron is written in an equation as $^{0}_{-1}\mathrm{e}$⁠: its mass number is zero and its charge $-1$⁠.

Step 4 of 8

Gamma rays

Gamma rays are photons, light of very high energy, far beyond ultraviolet and X-rays in the spectrum. A nucleus left with extra energy after alpha or beta decay gives it off as a gamma ray. The mass number and the atomic number do not change: it is the same nucleus, only with less energy. Choose Gamma and compare it with the other two kinds.

The three kinds of radiation reach different depths. Alpha particles are heavy and charged, and are stopped by a sheet of paper or a few centimetres of air. Beta particles get through paper and are stopped by a few millimetres of aluminium. Gamma rays are only weakened, by a thick layer of lead or concrete.

Step 5 of 8

No memory

The half-life of each isotope is fixed. Heat, pressure or a chemical reaction do not change it, because they do not touch the nucleus. And a nucleus has no age: every nucleus has the same chance of decaying in each second, for as long as it has not decayed. In a sample of $20$⁠ nuclei this shows clearly: the sample’s orange line jumps about the white curve.

Step 6 of 8

Activity

You cannot count the nuclei in a radioactive source, but you can count decays with a Geiger counter. The number of decays per second is the source’s activity, $A$⁠, measured in becquerels: 1 Bq is one decay per second. Here $A$⁠ is a different letter from the mass number; the context tells you which is meant.

If each nucleus has a chance $\lambda$⁠ of decaying in each second, then out of $N$⁠ nuclei an average of $\lambda N$⁠ decay each second:

$A = \lambda N$⁠

$\lambda$⁠ is the decay constant, in 1/s. It is tied to the half-life: $\lambda = \dfrac{\ln 2}{T_{1/2}}$$\lambda =$$\dfrac{\ln 2}{T_{1/2}}$⁠. The shorter the half-life, the greater the chance of decaying in each second. In the Scene, Half-life and Nuclei in the sample are locked.

Step 7 of 8

The activity falls

The activity is proportional to the number of nuclei left. So it too halves every half-life, and the decay curve can be read as a curve of the activity as well. This is how a hospital follows a radioactive substance given to a patient: it measures the activity rather than counting nuclei.

Step 8 of 8

Choosing a half-life

In medicine an isotope is chosen by its activity: enough decays to make an image, and not too much radiation for the patient. Here the number of nuclei is fixed, and the choice is the half-life.