Describe the emission of radiation from a nucleus as spontaneous and random in direction

5.2 – The Three Types of Nuclear Emission

Objective

Describe the emission of radiation from a nucleus as spontaneous and random in direction (isotropic) – a core AO1 requirement of the Cambridge IGCSE 0625 syllabus.

Key Concepts

• Spontaneous decay: an unstable or excited nucleus lowers its energy by emitting a particle or photon without any external trigger.
• Random (isotropic) direction: each decay has an equal probability of emitting into any solid angle; over many decays the radiation field is uniform in all directions.
• The syllabus focuses on three principal emissions: alpha (α), beta (β) and gamma (γ) radiation.

Why Emission Is Spontaneous

A nucleus in an unstable state possesses excess energy. Quantum‑mechanically it can reduce this energy by emitting a particle or photon. The probability per unit time that a particular nucleus will decay is constant, giving the exponential decay law

\[ N(t)=N_{0}\,e^{-\lambda t} \]

where N₀ is the initial number of nuclei, N(t) the number remaining after time t, and λ the decay constant – a property of the nuclide that cannot be altered by temperature, pressure, chemical state, etc. Hence the process is inherently spontaneous.

Random Direction of Emission

• The nucleus is effectively a point source compared with the wavelength of the emitted particle or photon.
• There is no internal or external axis that favours any particular direction, so each decay has the same probability of emitting into any element of solid angle 4π sr.
• Consequently, a large number of decays produce a uniform spherical pattern – an isotropic distribution.

Experimental Evidence of Isotropy

1. Place a thin foil of radioactive material at the centre of a spherical array of identical detectors.
2. Record the count in each detector for a sufficiently long period.
3. The counts in all detectors are statistically equal (within Poisson fluctuations), confirming that emission is random and isotropic.

Nature of the Three Emissions

In the syllabus:

• Alpha (α) particles are helium nuclei (⁴₂He).
• Beta (β) particles are electrons (β⁻) or positrons (β⁺); β⁻ is the routine decay mode, β⁺ is only a supplement.
• Gamma (γ) rays are high‑energy photons emitted from an excited daughter nucleus.

Comparison of the Three Emissions

Emission	Particle / Photon	Charge	Mass (u)	Relative Penetrating Ability	Typical Energy (MeV)	Relative Ionising Effect	Effect on Nucleus (ΔA, ΔZ)
Alpha (α)	Helium nucleus (42α)	+2 e	4.0026	Stopped by ≈0.5 mm paper (≈0.05 g cm⁻²) – lowest	4 – 9	Very high (α ≫ β > γ)	A ↓ 2, Z ↓ 2
Beta (β)	Electron (β⁻) or positron (β⁺)	–1 e (β⁻) or +1 e (β⁺)	≈0 (9.1 × 10⁻³¹ kg)	Stopped by ≈3 mm aluminium (≈0.8 g cm⁻²) – intermediate	0.01 – 3	Medium (α ≫ β > γ)	β⁻: A unchanged, Z ↑ 1 β⁺: A unchanged, Z ↓ 1
Gamma (γ)	High‑energy photon	0	0	Requires ≈2 cm lead (≈16 g cm⁻²) for ≈50 % attenuation – highest	0.1 – 10	Low (α ≫ β > γ)	A unchanged, Z unchanged (usually follows α or β decay)

Concise comparative statement:
Ionising effect – α ≫ β > γ.
Penetrating ability – γ ≫ β > α.

Representative Decay Equations

Alpha decay of uranium‑238

\[ ^{238}_{92}\text{U}\;\rightarrow\;^{234}_{90}\text{Th}\;+\;^{4}_{2}\alpha \]

Beta‑minus decay of carbon‑14

\[ ^{14}_{6}\text{C}\;\rightarrow\;^{14}_{7}\text{N}\;+\;\beta^{-}\;+\;\bar{u}_{e} \]

Gamma emission following beta decay of cobalt‑60

\[ ^{60}_{27}\text{Co}\;\rightarrow\;^{60}_{28}\text{Ni}\;+\;\beta^{-}\;+\;\gamma \]

Implications for Safety and Shielding

• Because each emission is unpredictable, shielding must protect from radiation arriving from any direction.
• Choice of shielding material follows the relative penetrating ability:
  • α – light material (e.g., a sheet of paper or a few centimetres of air).
  • β – low‑Z material such as plastic or a few millimetres of aluminium.
  • γ – dense, high‑Z material such as lead or several centimetres of concrete.
• The ionising effect follows the order α ≫ β > γ, so α particles produce the most severe local ionisation, β moderate, and γ the least.

Summary

Nuclear emissions are inherently spontaneous; a nucleus decays because it can lower its energy, not because of any external trigger. The emitted particle or photon leaves the nucleus in a random direction, giving an isotropic radiation field. Understanding the three main types—α, β and γ—allows us to predict the changes to the nucleus (ΔA, ΔZ), compare their relative ionising effects and relative penetrating abilities, and select appropriate shielding for safety.