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
- Bremsstrahlung (Braking Radiation): Electrons accelerated by a high voltage hit a metal target and are suddenly decelerated, emitting a continuous spectrum of X‑rays.
- 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.
- 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
| Application | Typical Energy (keV) | Key Feature |
|---|
| Medical imaging (X‑ray radiography) | 20–120 | High penetration, low dose |
| Industrial non‑destructive testing | 100–300 | Detects cracks, voids |
| Security scanning (airports) | 50–150 | Penetrates 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.