A half-life of 5 seconds means that after 5 seconds, half of the original number of radioactive nuclei in a sample will have decayed into other elements or isotopes. This decay is a random process; we cannot predict which individual nucleus will decay at any given time. However, we can predict the probability of decay within a given time interval.

Over time, the number of radioactive nuclei in the sample decreases exponentially. Each half-life represents a halving of the remaining radioactive nuclei. After 5 seconds, 50% remain; after 10 seconds, 25% remain; after 15 seconds, 12.5% remain, and so on. This exponential decay is a direct consequence of the spontaneous and random nature of the decay process.

The emission of radiation is random in direction because the decay occurs within the nucleus, and the emitted particles are not constrained by any external forces or a specific orientation. The nucleus is a very small, dense object. The emitted particles (alpha, beta, or gamma) are released from within this nucleus and travel outwards. There is no 'center' from which the radiation is emitted in a particular direction. The probability of detecting a particle in any given direction is uniform, reflecting the isotropic nature of the decay process within the nucleus. The nucleus itself doesn't have a preferred direction of decay; it's a random event occurring within the confines of the nucleus, leading to a random distribution of emitted radiation.

Alpha Particles: Alpha particles (⁴He nuclei, charge +2e, mass approximately 4 amu) are relatively massive and have a positive charge. When an alpha particle enters a uniform electric field, it is deflected towards the negative plate. The magnitude of the deflection is directly proportional to the charge of the particle (greater charge, greater deflection) and inversely proportional to its mass (less mass, greater deflection). The stronger the electric field, the greater the deflection. The deflection is also affected by the velocity of the alpha particle; a higher velocity results in a larger deflection.

When an alpha particle enters a uniform magnetic field, it experiences a force perpendicular to both its velocity and the magnetic field. This causes the alpha particle to move in a curved path. The direction of the deflection can be determined using the right-hand rule (thumb points in the direction of velocity, fingers point in the direction of the magnetic field, and the direction your palm faces is the direction of the force). The magnitude of the deflection is proportional to the charge of the particle, the speed of the particle, and the strength of the magnetic field. The mass of the particle is also a factor; a heavier particle will be deflected less. A higher velocity will result in a larger radius of curvature.

Beta Particles: Beta particles (e^- or e⁺, charge -1e or +1e, mass approximately 1/1836 amu) are electrons or positrons, respectively. They behave similarly to alpha particles in electric fields, being deflected towards the positive plate. The factors affecting deflection are the same as for alpha particles: charge, mass, and electric field strength.

In magnetic fields, beta particles also experience a curved path. The direction of deflection is again determined by the right-hand rule. The magnitude of the deflection is proportional to the charge, speed, and magnetic field strength, and inversely proportional to the mass. Because beta particles are much lighter than alpha particles, they are deflected more significantly by the magnetic field.

Gamma Radiation: Gamma radiation consists of photons, which are uncharged particles. Therefore, gamma radiation is not deflected by an electric or magnetic field. This is because the force on a charged particle is given by F = q(E + v x B), and since q = 0 for a photon, the force is zero. Gamma radiation travels in a straight line.

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.