## 21.5 PAIR ANNIHILATION This section describes the process of pair annihilation, where matter and antimatter convert into energy, serving as the reverse process of pair production. ### Definition Pair annihilation is a process in which a particle (like an electron) and its corresponding antiparticle (a positron) collide, resulting in their mutual destruction. Their total mass is converted into energy in the form of two or more high-energy photons (gamma rays). ### Reverse of Pair Production * **Pair Production:** Energy (photon) $\rightarrow$ Mass (electron + positron). * **Pair Annihilation:** Mass (electron + positron) $\rightarrow$ Energy (two photons). ### Conservation Laws The process must adhere to fundamental conservation laws: * **Conservation of Energy:** The total energy of the resulting photons is equal to the sum of the rest mass energies and kinetic energies of the initial electron-positron pair. * **Conservation of Momentum:** To conserve momentum, at least two photons must be created. If the initial pair has zero net momentum, the two photons are emitted in opposite directions, ensuring the final net momentum is also zero. A single photon cannot be produced as it would violate momentum conservation. ### Energy of Emitted Photons * If the electron and positron are approximately at rest before annihilation, the total energy is just their combined rest mass energy ($2m_0c^2$). This energy is split equally between the two resulting photons. * The energy of each photon is $E = hf = m_{0} c^{2} = 0.511 \mathrm{MeV}$. * The general formula, including kinetic energy (K.E.), is: $$ 2 m_{0} c^{2}+K \cdot E_{\text {electron }}+K \cdot E_{\text {positron }}=\text { Energy of two gamma photons} \quad (21.13) $$ ### Illustration ### Other Examples Annihilation is not limited to electrons and positrons. Other examples include proton-antiproton annihilation and Higgs production. ### Significance Pair annihilation provides strong experimental confirmation of Einstein's theory of mass-energy equivalence ($E=mc^2$) and the photon model of electromagnetic radiation. | Key Formula/Value | Description | | --------------------------------- | --------------------------------------------------------------------------- | | $E = m_0 c^2 = 0.511 \text{ MeV}$ | The rest mass energy of an electron or positron, and the energy of each photon produced from a stationary pair. | | $2m_0c^2 + K.E._{total} = E_{\gamma_1} + E_{\gamma_2}$ | The general energy conservation equation for pair annihilation. |