Types of Radioactive Decay: Alpha, Beta, and Gamma
- You're holding a piece of uranium ore in your hand.
- Though it appears unremarkable, deep within its atoms, a remarkable transformation is taking place.
- The uranium nuclei are unstable, and they spontaneously emit particles and energy in a process called radioactive decay, which allows unstable nuclei to become more stable.
Alpha Decay: Emission of Helium Nuclei
Alpha decay
Alpha decay occurs when an unstable nucleus emits an alpha particle, which is essentially a helium nucleus made up of two protons and two neutrons ($^4_2 \text{He}$).
This emission reduces both the proton number ($Z$) and the nucleon number ($A$) of the parent nucleus, producing a new element.
- Consider uranium-235 ($^{235}_{92} \text{U}$), which undergoes alpha decay to form thorium-231 ($^{231}_{90} \text{Th}$): $$
^{235}_{92} \text{U} \rightarrow ^{231}_{90} \text{Th} + ^4_2 \text{He}
$$ - Here’s what happens:
- The proton number ($Z$) decreases by 2: $92 \rightarrow 90$.
- The nucleon number ($A$) decreases by 4: $235 \rightarrow 231$.
Energy Released During Alpha Decay
- The energy released in alpha decay comes from the mass defect, the difference in mass between the parent nucleus and the products.
- Using Einstein’s equation, $E = mc^2$, you can calculate this energy.
For instance, if the mass difference ($\Delta m$) is 0.0046 u, the energy released is:
$$
E = \Delta m \cdot 931.5 \, \text{MeV u}^{-1} = 0.0046 \cdot 931.5 \, \text{MeV} \approx 4.3 \, \text{MeV}.
$$
This energy is carried away as the kinetic energy of the alpha particle and the recoiling daughter nucleus.
Alpha particles are highly ionizing but have low penetration power, they can be stopped by a sheet of paper or a few centimeters of air.
Beta Decay: Conversion of Neutrons or Protons
Beta Minus ($\beta^-$) Decay
Beta minus decay
In beta minus decay, a neutron in the nucleus is converted into a proton, emitting an electron ($\beta^-$) and an antineutrino ($\bar{\nu}$):
$$
n \rightarrow p + e^- + \bar{\nu}
$$
This increases the proton number ($Z$) by 1 while the nucleon number ($A$) remains unchanged.
- For thorium-234 decay: $$
^{234}_{90} \text{Th} \rightarrow ^{234}_{91} \text{Pa} + e^- + \bar{\nu}
$$ - Here:
- The proton number ($Z$) increases by 1: $90 \rightarrow 91$.
- The nucleon number ($A$) remains $234$.
Beta Plus ($\beta^+$) Decay
Beta plus decay
In beta plus decay, a proton is converted into a neutron, emitting a positron ($\beta^+$) and a neutrino($\nu$):
$$
p \rightarrow n + e^+ + \nu
$$
This decreases the proton number ($Z$) by 1 while the nucleon number ($A$) remains unchanged.
Sodium-22 decay:
$$
^{22}_{11} \text{Na} \rightarrow ^{22}_{10} \text{Ne} + e^+ + \nu
$$
Why Do Beta Particles Have a Continuous Energy Spectrum?
- Unlike alpha particles, which have a fixed energy, the electrons or positrons emitted in beta decay exhibit a continuous energy spectrum.
- This puzzled scientists until Wolfgang Pauli proposed the existence of the neutrino, a nearly massless, neutral particle that shares the released energy with the electron or positron.
The neutrino was later confirmed experimentally and is essential for conserving energy and angular momentum in beta decay.
Gamma Decay: Emission of High-Energy Photons
What is Gamma Decay?
Gamma decay
Gamma decay occurs when an excited nucleus releases excess energy by emitting a gamma ray, a high-energy photon.
Unlike alpha and beta decay, gamma decay does not alter the proton number ($Z$) or the nucleon number ($A$) of the nucleus.
- After undergoing beta decay, cobalt-60 ($^{60}_{27} \text{Co}$) produces a daughter nucleus ($^{60}_{28} \text{Ni}$) in an excited state.
- The nucleus then releases energy by emitting a gamma photon:
$$
^{60}_{28} \text{Ni}^* \rightarrow ^{60}_{28} \text{Ni} + \gamma
$$
Properties of Gamma Rays
- Gamma rays are massless and uncharged.
- They are the most penetrating type of radiation, requiring thick lead or concrete to block.
Gamma decay often accompanies alpha or beta decay as the nucleus transitions to a more stable energy state.
The Role of Neutrinos and Antineutrinos in Beta Decay
Why Were Neutrinos Postulated?
- In beta decay, the emitted electron or positron does not account for all the energy released.
- To conserve energy and momentum, physicists hypothesized the existence of neutrinos and antineutrinos.
Properties of Neutrinos
- Electrically neutral.
- Extremely small mass (nearly zero).
- Weakly interacting with matter, making them very difficult to detect.
- What changes occur to the proton number ($Z$) and nucleon number ($A$) during alpha decay?
- Why do beta particles have a continuous energy spectrum?
- How do gamma rays differ fundamentally from alpha and beta particles?
