understand that an antiparticle has the same mass but opposite charge to the corresponding particle, and that a positron is the antiparticle of an electron

Antiparticles

In modern particle physics every fundamental particle has a corresponding antiparticle. The antiparticle shares the same rest mass as its partner but carries opposite electric charge and other quantum numbers (such as lepton number, baryon number, etc.).

Key Properties

• Identical rest mass: \$m{\text{particle}} = m{\text{antiparticle}}\$
• Opposite electric charge: \$q{\text{antiparticle}} = -\,q{\text{particle}}\$
• Opposite quantum numbers (e.g., lepton number \$L\$, baryon number \$B\$)
• Same spin and intrinsic angular momentum

Particle–Antiparticle Table

The Positron (\$e^{+}\$)

The positron is the antiparticle of the electron. It has the same mass as an electron (\$0.511\ \text{MeV}/c^{2}\$) but carries a positive elementary charge \$+1\,e\$.

Discovery

Positrons were first observed by Carl Anderson in 1932 while studying cosmic rays. Their tracks in a cloud chamber curved opposite to those of electrons in a magnetic field, confirming the opposite charge.

Positron Annihilation

When a positron encounters an electron, they can annihilate, converting their mass into energy in the form of photons. The simplest annihilation reaction is:

\$e^{-} + e^{+} \;\rightarrow\; \gamma + \gamma\$

Each photon carries an energy of \$511\ \text{keV}\$, corresponding to the rest mass energy of the electron (or positron).

Applications

• Positron Emission Tomography (PET): A medical imaging technique that detects the \$511\ \text{keV}\$ photons from positron annihilation to produce detailed images of metabolic activity.
• Material studies using positron annihilation spectroscopy to probe defects in solids.
• Fundamental tests of charge–parity (CP) symmetry.

Conceptual Understanding

To master the objective, students should be able to:

1. State that an antiparticle has the same mass as its corresponding particle.
2. Explain why the electric charge is opposite for particle–antiparticle pairs.
3. Identify the positron as the antiparticle of the electron and list its key properties.
4. Describe the annihilation process and calculate the energy of the resulting photons using \$E = mc^{2}\$.

Sample Question

Q: A positron with kinetic energy \$200\ \text{keV}\$ annihilates with a stationary electron. Calculate the total energy of each photon produced, assuming the annihilation results in two photons.

A: Total energy of each photon = rest‑mass energy + kinetic energy shared equally.

Rest‑mass energy of electron = \$511\ \text{keV}\$.

Total initial energy = \$511\ \text{keV} + 511\ \text{keV} + 200\ \text{keV} = 1222\ \text{keV}\$.

Energy per photon = \$\dfrac{1222\ \text{keV}}{2} = 611\ \text{keV}\$.