E.3 Radioactive decay

Radioactive decay is defined by two fundamental characteristics that must both be correctly identified.

Spontaneous means decay occurs without any external trigger. No heat, pressure, or chemical change can cause or prevent it — the nucleus decays entirely on its own.

Random means it is impossible to predict exactly when any specific nucleus will decay. Each nucleus has a fixed probability of decaying per unit time, but the exact moment is uncertain.

The correct pair is spontaneous and random. While individual decays are unpredictable, large samples follow precise statistical (exponential) laws.

We need the two properties that define radioactive decay.

Decay is never stimulated by external conditions, and individual decays are never predictable. Both words are wrong, so this option is eliminated.

While random is correct, decay is not stimulated — it is spontaneous. This option is eliminated.

While spontaneous is correct, individual nuclear decays are not predictable — this is a fundamental quantum mechanical feature. This option is eliminated.

Spontaneous and random is the only option with both words correctly describing radioactive decay.

An alpha particle is identical to a helium-4 nucleus: ${}_2^4\text{He}$. It consists of 2 protons and 2 neutrons.

Since the alpha particle carries away 4 nucleons, the mass number $A$ of the parent nucleus decreases by 4.

Since the alpha particle carries away 2 protons, the atomic number $Z$ of the parent nucleus decreases by 2.

The correct description is: mass number decreases by 4, atomic number decreases by 2.

We need to find the correct changes to $A$ and $Z$ during alpha decay, given that ${}_2^4\text{He}$ is emitted.

This reverses the numbers. The alpha particle has $A=4$ and $Z=2$, not $A=2$ and $Z=4$. Eliminated.

If the alpha particle ($A=4$) is emitted, the mass number cannot remain unchanged. Eliminated.

The alpha particle carries 2 protons, so the atomic number must decrease by 2, not remain unchanged. Eliminated.

Mass number decreases by 4, atomic number decreases by 2 is the only consistent option.