An atomic nucleus consists of protons and neutrons, and unstable nuclei decay by emitting radiation. We study the properties of α, β, and γ decay.
Basic Knowledge
Notation for an atomic nucleus: ₍Z₎^A X（X: element symbol, A: mass number, Z: number of protons）
Number of neutrons N = A − Z
Isotopes: Nuclei with the same Z but different A.
Three types of radiation:
① α rays: Emission of ₂⁴He (a helium nucleus). Strong ionizing power and weak penetrating power.₍Z₎^A X → ₍Z-2₎^(A-4) Y + ₂⁴He
② β rays: Emission of an electron (β⁻) (neutron → proton + electron + antineutrino).₍Z₎^A X → ₍Z+1₎^A Y + e⁻ + ν̄
③ γ rays: Emission of high-energy electromagnetic waves. Strongest penetrating power and weak ionizing power.
Units of radioactivity: Bq (becquerel) = 1 decay/second, Sv (sievert) = amount of effect on living organisms
Mass number A and proton number Z（A = Z + N. Specify the type of nucleus）
α decay（Z decreases by 2 and A decreases by 4. A helium nucleus is emitted）
β decay（Z increases by 1 and A remains unchanged. An electron is emitted）
γ decay（Z and A remain unchanged. A high-energy photon is emitted from an excited nucleus）
Half-life T₁/₂（the time required for the number of radioactive isotopes to decrease by half）
Bq (becquerel) and Sv (sievert)（units of radioactivity strength/effect on living organisms）
Further Exploration (Background and Significance)
Half-life T₁/₂: Remaining amount N(t) = N₀ × (1/2)^(t/T₁/₂) = N₀ e^(−λt)（λ: decay constant）. T₁/₂ = ln2/λ ≈ 0.693/λ.
Because the half-life is constant regardless of the substance, temperature, or pressure, it is used for radiometric dating（such as carbon ¹⁴C dating）. The half-life of ¹⁴C is approximately 5730 years, and it is widely used in archaeology and paleontology.
Approximate penetrating power of the three types of radiation:
・α rays: several cm in air; stopped by one sheet of paper
・β rays: stopped by several mm of aluminum
・γ rays: thick plates of lead or concrete are required
Pauli predicted the emission of neutrinos in β decay in 1930, and it was later confirmed experimentally.
- α decay: Z → Z−2, A → A−4
- β decay: Z → Z+1, A unchanged
- γ decay: Z and A unchanged
- Penetrating power: γ > β > α
- Ionizing power: α > β > γ
- Half-life: N = N₀(1/2)^(t/T₁/₂)
- ¹⁴C half-life ≈ 5730 years (used for dating)
Notes (Easily Confused Points)
① In α and β decay, Z changes → the element changes (transmutation). ② In γ decay, Z and A do not change (the element remains the same, and the excitation energy of the nucleus becomes a photon). ③ Penetrating power and ionizing power have an inverse relationship. ④ Half-lives vary widely, from less than ps to several billion years, depending on the type.
Practice
- When ²³⁸₉₂U undergoes α decay, find the mass number and proton number of the resulting nucleus.
- What fraction of its original amount remains after 24 days for ¹³¹I with a half-life of 8 days?
- Arrange α, β, and γ rays in order of decreasing penetrating power, and write the identity of each ray.