The emission of radiation from a nucleus is considered a quantum mechanical phenomenon because it occurs at a very small scale, involving particles behaving in ways that are not described by classical physics. Classical physics predicts a continuous spectrum of energy, but radioactive decay involves discrete, quantized amounts of energy being emitted as specific particles (alpha, beta, or gamma).

This quantization is a fundamental aspect of quantum mechanics. The energy of the emitted radiation is precisely determined and cannot take on any arbitrary value. Furthermore, the exact time of decay is unpredictable, which is another hallmark of quantum behavior.

The uncertainty principle, formulated by Werner Heisenberg, plays a crucial role. The uncertainty principle states that it is fundamentally impossible to know both the exact position and the exact momentum of a particle simultaneously. In the context of radioactive decay, this means we cannot predict precisely when a specific nucleus will decay. The decay time is governed by a probability distribution, and the uncertainty principle reflects the inherent uncertainty in the system's state. The nucleus exists in a state of potential energy, and the emission of radiation is a transition to a lower energy state. The uncertainty principle dictates the timescale of this transition.

Alpha (α) particles: These are helium nuclei (⁴He), consisting of 2 protons and 2 neutrons.

• Nature: They are relatively heavy and positively charged.
• Ionising effect: They have a high ionising effect because of their large charge and mass. They interact strongly with matter, knocking electrons off atoms in their path.
• Penetrating ability: They have a low penetrating ability. They can be stopped by a sheet of paper or even a few centimetres of air.

Beta (β−) particles: These are high-energy electrons emitted from the nucleus.

• Nature: They are electrons with a negative charge.
• Ionising effect: They have a moderate ionising effect, less than alpha particles but more than gamma rays. They interact with electrons in the atoms they pass through.
• Penetrating ability: They have a better penetrating ability than alpha particles, but less than gamma rays. They can be stopped by a thin sheet of metal (e.g., aluminium).

Gamma (γ) rays: These are high-energy electromagnetic radiation (photons).

• Nature: They are a form of electromagnetic radiation, similar to X-rays. They have no mass or charge.
• Ionising effect: They have a low ionising effect. They interact with matter through electromagnetic forces, but do not knock electrons off atoms as effectively as alpha or beta particles.
• Penetrating ability: They have a high penetrating ability. They can pass through a significant thickness of matter, such as lead or concrete.

The relationship between the radius of curvature (r) of a charged particle in a magnetic field (B) is given by:

r = mv / (qB)

where:

• r is the radius of curvature.
• m is the mass of the particle.
• v is the speed of the particle.
• q is the charge of the particle.
• B is the strength of the magnetic field.

Velocity in this context refers to the speed of the charged particle as it moves through the magnetic field. It is a vector quantity, indicating both the speed and direction of the particle's motion.

Radius of curvature is the radius of the circular path that a charged particle follows when moving perpendicularly to a uniform magnetic field. It is a measure of how sharply the particle is deflected. A larger radius of curvature indicates a less sharp deflection, while a smaller radius of curvature indicates a more sharp deflection. The radius of curvature is directly proportional to the mass of the particle and the velocity, and inversely proportional to the charge and the magnetic field strength.