AP Physics 2- 15.8 Types of Radioactive Decay- Study Notes- New Syllabus
AP Physics 2- 15.8 Types of Radioactive Decay – Study Notes
AP Physics 2- 15.8 Types of Radioactive Decay – Study Notes – per latest Syllabus.
Key Concepts:
- Subatomic Particles in Radioactive Decay
- Types of Radioactive Decay
Subatomic Particles in Radioactive Decay
During radioactive decay, nuclei can emit subatomic particles with unique properties. These particles help conserve energy, charge, and lepton number during nuclear transformations.
Alpha (\(\boldsymbol{\alpha}\)) Particles
An \(\alpha\)-particle is a helium nucleus consisting of 2 protons and 2 neutrons.
- Symbol: \(\mathrm{^4_2He \, \text{or He}^{2+}}\)
- Only \(\mathrm{He-4}\) nuclei are considered in Physics 2.
- \(\alpha\)-particles are emitted in \(\alpha\)-decay from heavy nuclei and are highly ionizing but weakly penetrating.
Neutrinos and Antineutrinos
\(\nu_e\) (neutrino) and \(\bar{\nu}_e\) (antineutrino) are electrically neutral subatomic particles with negligible mass.
- Interact with matter only via the weak nuclear force and gravity.
- Because of their weak interactions, they pass through normal matter almost unaffected.
- Emitted during \(\beta\)-decay processes to conserve energy and lepton number.
Positrons (\(\boldsymbol{e^+}\))
A positron is the antiparticle of an electron.
- Electric charge: \(+1\), mass equal to an electron.
- Symbol: \(\mathrm{e^+ \, \text{or } \beta^+}\)
- Emitted during \(\beta^+\)-decay (positron emission) when a proton converts into a neutron in the nucleus.
Key Features:
- \(\alpha\)-particles: helium nuclei, 2 protons + 2 neutrons, highly ionizing.
- Neutrinos and antineutrinos: neutral, nearly massless, interact very weakly with matter.
- Positrons: positively charged electrons, same mass as electrons, emitted in \(\beta^+\)-decay.
Example :
Identify the type of particle emitted in the following decay: a proton in the nucleus converts into a neutron.
▶️ Answer/Explanation
Step 1: Proton converts to neutron → \(\beta^+\)-decay.
Step 2: Particle emitted is a positron (\(\mathrm{e^+}\)) and a neutrino (\(\nu_e\)) to conserve lepton number.
Example :
Describe the composition of an alpha particle emitted in nuclear decay.
▶️ Answer/Explanation
Step 1: An \(\alpha\)-particle is a helium nucleus.
Step 2: Composition: 2 protons + 2 neutrons (\(\mathrm{^4_2He}\) or \(\mathrm{He}^{2+}\)).
Types of Radioactive Decay
Radioactive decay is the spontaneous transformation of an unstable nucleus into a more stable nucleus. During decay, subatomic particles or photons are emitted. All nuclear decays obey the conservation laws for nucleon number, lepton number, and charge.
Conservation Laws in Nuclear Decay
- Nucleon number: Total number of protons and neutrons remains constant.
- Charge: Total electric charge is conserved.
- Lepton number: Total number of leptons (electrons, positrons, neutrinos, antineutrinos) is conserved.
Alpha (\(\boldsymbol{\alpha}\)) Decay
Occurs when a nucleus ejects an \(\alpha\)-particle (helium nucleus, \(\mathrm{^4_2He}\) or \(\mathrm{He}^{2+}\)). Reduces atomic number by 2 and mass number by 4:
$ \mathrm{^A_Z X \to ^{A-4}_{Z-2} Y + ^4_2He} $
- Typical for heavy nuclei (e.g., uranium, thorium).
- \(\alpha\)-particles are highly ionizing but weakly penetrating.
Beta-minus (\(\boldsymbol{\beta^-}\)) Decay
Occurs when a neutron converts into a proton. Emission of an electron (\(\beta^-\)) and an antineutrino (\(\bar{\nu}_e\)) conserves charge and lepton number:
$ \mathrm{^A_Z X \to ^A_{Z+1} Y + \beta^- + \bar{\nu}_e} $
- Mass number remains the same, atomic number increases by 1.
- \(\beta^-\)-particles are moderately ionizing and moderately penetrating.
Beta-plus (\(\boldsymbol{\beta^+}\)) Decay / Positron Emission
Occurs when a proton converts into a neutron. Emission of a positron (\(\beta^+\) or \(\mathrm{e^+}\)) and a neutrino (\(\nu_e\)) conserves charge and lepton number:
$ \mathrm{^A_Z X \to ^A_{Z-1} Y + \beta^+ + \nu_e} $
- Mass number remains the same, atomic number decreases by 1.
- Positrons annihilate with electrons when they interact with matter.
Gamma (\(\boldsymbol{\gamma}\)) Decay
Occurs when an excited nucleus releases excess energy as a photon (\(\gamma\)) without changing mass or atomic number:
$ \mathrm{^A_Z X^* \to ^A_Z X + \gamma} $
- Usually follows \(\alpha\) or \(\beta\)-decay.
- Gamma rays are weakly ionizing but highly penetrating.
Key Note:
- The type of decay depends on the isotope of the element.
- All decays obey conservation of nucleon number, lepton number, and charge.
- \(\alpha\): heavy nuclei, reduces mass and atomic number, highly ionizing.
- \(\beta^-\): neutron → proton, emits electron + antineutrino.
- \(\beta^+\): proton → neutron, emits positron + neutrino.
- \(\gamma\): nucleus de-excites, emits photon, no change in mass or atomic number.
Example :
A polonium-210 nucleus undergoes \(\alpha\)-decay. Write the daughter nucleus.
▶️ Answer/Explanation
Step 1: Alpha decay equation: \(\mathrm{^{210}_{84}Po \to ^{206}_{82}Pb + ^4_2He}\)
Step 2: Interpretation: Atomic number decreases by 2, mass number decreases by 4.
Example :
A carbon-11 nucleus undergoes \(\beta^+\)-decay. Determine the daughter nucleus.
▶️ Answer/Explanation
Step 1: Beta-plus decay equation: \(\mathrm{^{11}_6 C \to ^{11}_5 B + \beta^+ + \nu_e}\)
Step 2: Interpretation: Atomic number decreases by 1, mass number remains 11. Positron and neutrino are emitted.
Example :
An excited cobalt-60 nucleus emits a gamma photon after beta decay. Write the gamma decay process.
▶️ Answer/Explanation
Step 1: Gamma decay equation: \(\mathrm{^{60}_27 Co^* \to ^{60}_27 Co + \gamma}\)
Step 2: Interpretation: Mass and atomic numbers remain unchanged. Excess energy is emitted as a photon.