Radioactivity

Cheatsheet Content

### Radioactivity Basics - **Definition**: Spontaneous emission of radiation from an unstable atomic nucleus. - **Nucleus Stability**: Determined by neutron-to-proton ratio. Too many/few neutrons lead to instability. - **Decay Series**: A sequence of radioactive decays until a stable nuclide (atom) is formed. - **Half-Life ($T_{1/2}$)**: Time required for half of the radioactive nuclei in a sample to decay. - Formula: $N(t) = N_0 e^{-\lambda t}$ where $\lambda = \frac{\ln(2)}{T_{1/2}}$ - $N(t)$: number of nuclei remaining at time $t$ - $N_0$: initial number of nuclei - $\lambda$: decay constant ### Alpha ($\alpha$) Decay - **Nature**: Emission of an alpha particle ($^4_2\text{He}$ nucleus, 2 protons, 2 neutrons). - **Penetration**: Low (stopped by paper, skin). - **Ionization**: High. - **Equation**: $^A_Z X \rightarrow ^{A-4}_{Z-2} Y + ^4_2\text{He}$ - **Example**: Uranium-238 decaying to Thorium-234: $$^{238}_{92}\text{U} \rightarrow ^{234}_{90}\text{Th} + ^4_2\text{He}$$ ### Beta ($\beta$) Decay - **Nature**: Emission of a beta particle (electron or positron). - **Penetration**: Medium (stopped by aluminum). - **Ionization**: Medium. #### Beta-Minus ($\beta^-$) Decay - **Process**: Neutron converts into a proton, emitting an electron ($e^-$ or $^0_{-1}\beta$) and an antineutrino ($\bar{\nu}_e$). - **Equation**: $^A_Z X \rightarrow ^A_{Z+1} Y + ^0_{-1} e + \bar{\nu}_e$ - **Example**: Carbon-14 decaying to Nitrogen-14: $$^{14}_6\text{C} \rightarrow ^{14}_7\text{N} + ^0_{-1}e + \bar{\nu}_e$$ #### Beta-Plus ($\beta^+$) Decay (Positron Emission) - **Process**: Proton converts into a neutron, emitting a positron ($e^+$ or $^0_{+1}\beta$) and a neutrino ($\nu_e$). - **Equation**: $^A_Z X \rightarrow ^A_{Z-1} Y + ^0_{+1} e + \nu_e$ - **Example**: Oxygen-15 decaying to Nitrogen-15: $$^{15}_8\text{O} \rightarrow ^{15}_7\text{N} + ^0_{+1} e + \nu_e$$ ### Gamma ($\gamma$) Decay - **Nature**: Emission of high-energy electromagnetic radiation (gamma photon, $\gamma$). - **Process**: Occurs when a nucleus in an excited state (often after $\alpha$ or $\beta$ decay) transitions to a lower energy state. No change in atomic number or mass number. - **Penetration**: High (stopped by lead or thick concrete). - **Ionization**: Low. - **Equation**: $^A_Z X^* \rightarrow ^A_Z X + \gamma$ (where $X^*$ is an excited nucleus) - **Example**: Cobalt-60 decaying to Nickel-60 (excited), then to Nickel-60 (ground state) plus a gamma ray: $$^{60}_{27}\text{Co} \rightarrow ^{60}_{28}\text{Ni}^* + ^0_{-1}e + \bar{\nu}_e$$ $$^{60}_{28}\text{Ni}^* \rightarrow ^{60}_{28}\text{Ni} + \gamma$$ ### Other Decay Modes #### Electron Capture (EC) - **Process**: An inner orbital electron is captured by the nucleus, converting a proton into a neutron and emitting a neutrino. - **Equation**: $^A_Z X + ^0_{-1}e \rightarrow ^A_{Z-1} Y + \nu_e$ - **Result**: Similar to $\beta^+$ decay (decreases atomic number by 1), but no positron emitted. #### Spontaneous Fission - **Process**: A heavy nucleus splits into two or more smaller nuclei, releasing neutrons and energy. - **Example**: Specific isotopes of Uranium and Plutonium.