# Beta Minus and Beta Plus Decay ## Overview - Beta decay occurs via the **weak interaction** - One of the four fundamental forces in nature - Responsible for radioactive decay processes involving the transformation of quarks --- ## Beta-Minus Decay ### What is Beta-Minus Decay? - A **beta-minus** ($\beta^-$) particle is a high-energy electron emitted from the nucleus - In $\beta^-$ decay, a **neutron transforms into a proton**, emitting: - An electron ($e^-$) - An anti-electron neutrino ($\bar{\nu}_e$)

$\beta^-$ decay: $n \rightarrow p + e^- + \bar{\nu}_e$

### Effect on Nuclear Structure When a $\beta^-$ particle is emitted: - **Proton number increases by 1** (one more proton in the nucleus) - **Nucleon number remains the same** (total number of nucleons unchanged) ### General Equation $$^{A}_{Z}X \rightarrow ^{A}_{Z+1}Y + ^{0}_{-1}\beta + ^{0}_{0}\bar{\nu}_e$$ ### Example Consider carbon-14 undergoing $\beta^-$ decay to become nitrogen-14: $$^{14}_{6}C \rightarrow ^{14}_{7}N + ^{0}_{-1}\beta + ^{0}_{0}\bar{\nu}_e$$ - The carbon nucleus has 6 protons - After decay, the nitrogen nucleus has 7 protons - Total nucleons remain 14

The new nucleus after decay is called the "daughter" nucleus

--- ## Beta-Plus Decay ### What is Beta-Plus Decay? - A **beta-plus** ($\beta^+$) particle is a high-energy positron emitted from the nucleus - In $\beta^+$ decay, a **proton transforms into a neutron**, emitting: - A positron ($e^+$) – the antiparticle of the electron - An electron neutrino ($\nu_e$)

$\beta^+$ decay: $p \rightarrow n + e^+ + \nu_e$

### Effect on Nuclear Structure When a $\beta^+$ particle is emitted: - **Proton number decreases by 1** (one fewer proton in the nucleus) - **Nucleon number remains the same** (total number of nucleons unchanged) ### General Equation $$^{A}_{Z}X \rightarrow ^{A}_{Z-1}Y + ^{0}_{+1}\beta + ^{0}_{0}\nu_e$$ ### Example Consider carbon-12 undergoing $\beta^+$ decay to become boron-12: $$^{12}_{6}C \rightarrow ^{12}_{5}B + ^{0}_{+1}\beta + ^{0}_{0}\nu_e$$ - The carbon nucleus has 6 protons - After decay, the boron nucleus has 5 protons - Total nucleons remain 12 --- ## Quark Model of Beta-Minus Decay ### The Underlying Process - Recall: $\beta^-$ decay involves a neutron transforming into a proton - At the quark level, this occurs because a **down quark transforms into an up quark** ### Quark Compositions | Particle | Quark Composition | |----------|-------------------| | Neutron | $udd$ | | Proton | $uud$ | ### The Transformation The fundamental process at the quark level is: $$d \rightarrow u + e^- + \bar{\nu}_e$$ - A down quark ($d$) converts to an up quark ($u$) - This changes the neutron ($udd$) into a proton ($uud$) - An electron and anti-electron neutrino are emitted ### Visualizing the Change Starting particle (neutron): - Contains: up, down, down quarks - Total charge: $+\frac{2}{3}e - \frac{1}{3}e - \frac{1}{3}e = 0$ Ending particle (proton): - Contains: up, up, down quarks - Total charge: $+\frac{2}{3}e + \frac{2}{3}e - \frac{1}{3}e = +1e$ ### Charge Conservation **Left side of equation:** - Down quark charge: $-\frac{1}{3}e$ **Right side of equation:** - Up quark charge: $+\frac{2}{3}e$ - Electron charge: $-1e$ - Anti-electron neutrino charge: $0$ - Total: $+\frac{2}{3}e + (-1e) + 0 = -\frac{1}{3}e$ ✓

Charge is conserved in the quark transformation equation

--- ## Quark Model of Beta-Plus Decay ### The Underlying Process - Recall: $\beta^+$ decay involves a proton transforming into a neutron - At the quark level, this occurs because an **up quark transforms into a down quark** ### The Transformation The fundamental process at the quark level is: $$u \rightarrow d + e^+ + \nu_e$$ - An up quark ($u$) converts to a down quark ($d$) - This changes the proton ($uud$) into a neutron ($udd$) - A positron and electron neutrino are emitted ### Visualizing the Change Starting particle (proton): - Contains: up, up, down quarks - Total charge: $+\frac{2}{3}e + \frac{2}{3}e - \frac{1}{3}e = +1e$ Ending particle (neutron): - Contains: up, down, down quarks - Total charge: $+\frac{2}{3}e - \frac{1}{3}e - \frac{1}{3}e = 0$ ### Charge Conservation **Left side of equation:** - Up quark charge: $+\frac{2}{3}e$ **Right side of equation:** - Down quark charge: $-\frac{1}{3}e$ - Positron charge: $+1e$ - Electron neutrino charge: $0$ - Total: $-\frac{1}{3}e + (+1e) + 0 = +\frac{2}{3}e$ ✓

Charge is always conserved in quark transformation equations

--- ## Key Summary | Decay Type | Particle Change | Quark Change | Emitted Particles | Proton Number | Nucleon Number | |------------|----------------|--------------|-------------------|---------------|----------------| | $\beta^-$ | $n \rightarrow p$ | $d \rightarrow u$ | $e^-$ and $\bar{\nu}_e$ | Increases by 1 | Unchanged | | $\beta^+$ | $p \rightarrow n$ | $u \rightarrow d$ | $e^+$ and $\nu_e$ | Decreases by 1 | Unchanged |

Beta decay occurs via the weak interaction, not the electromagnetic or strong nuclear force