understand that annihilation occurs when a particle interacts with its antiparticle and that mass–energy and momentum are conserved in the process

Production and Use of X‑Rays

What are X‑Rays?

X‑rays are a form of high‑energy electromagnetic radiation with wavelengths between 0.01 nm and 10 nm. They are produced when charged particles, usually electrons, are accelerated or decelerated, or when a particle meets its antiparticle and annihilates.

How X‑Rays are Produced

  1. Bremsstrahlung (Braking Radiation): Electrons accelerated by a high voltage hit a metal target and are suddenly decelerated, emitting a continuous spectrum of X‑rays.
  2. Characteristic X‑Rays: When an inner‑shell electron is ejected, an outer‑shell electron drops down to fill the vacancy, releasing a photon of a fixed energy.
  3. Electron‑Positron Annihilation: An electron (\$e^-\$) meets its antiparticle, the positron (\$e^+\$). They annihilate, producing two gamma photons:

    \$e^- + e^+ \rightarrow \gamma + \gamma\$

    Each photon carries energy \$E = mc^2\$, where \$m\$ is the electron mass.

Conservation Laws in Annihilation

During annihilation, both mass–energy and momentum are conserved.

  • Energy: \$2m_ec^2\$ (total rest mass energy of the electron and positron) equals the sum of the energies of the two photons.
  • Momentum: The photons are emitted in opposite directions, so their momenta cancel, keeping the total momentum zero.

Analogy: Imagine two ice skaters pushing off each other. They move apart with equal and opposite speeds, keeping the centre of mass still.

Typical X‑Ray Tube Setup

High Voltage: Accelerates electrons to 20–150 kV.

🛠️ Target: Usually tungsten; electrons hit it, producing X‑rays.

🧊 Cooling: Water or air keeps the target from melting.

📐 Focusing: A cone of electrons ensures a small, sharp X‑ray beam.

Applications of X‑Rays

ApplicationTypical Energy (keV)Key Feature
Medical imaging (X‑ray radiography)20–120High penetration, low dose
Industrial non‑destructive testing100–300Detects cracks, voids
Security scanning (airports)50–150Penetrates luggage

Exam Tips

  • Remember the annihilation equation: \$e^- + e^+ \rightarrow \gamma + \gamma\$.
  • Use \$E = mc^2\$ to calculate photon energy from electron mass.
  • Show conservation of momentum: \$\vec{p}{\text{initial}} = \vec{p}{\text{final}}\$.
  • When asked to compare X‑ray production methods, list bremsstrahlung vs characteristic X‑rays.
  • Include typical voltage ranges for medical vs industrial X‑ray tubes.