X-rays

X-rays are high-energy electromagnetic waves with very short wavelengths (ranging from approximately $10^{-8} \text{ m}$ to $10^{-13} \text{ m}$) and high frequencies.

1. Production of X-rays (The X-ray Tube)

X-rays are produced when fast-moving electrons are suddenly stopped by a metal target of high melting point. This typically occurs in a specialized vacuum tube called the Coolidge X-ray Tube.

• Key Components:

  • Cathode (Filament): A heated tungsten filament that emits electrons through thermionic emission.

  • Anode (Target): A block of metal (e.g., Tungsten, Molybdenum) with a high melting point and high atomic number, set at an angle (usually $45^\circ$).

  • High Potential Difference (HV): A large potential difference (e.g., $10 \text{ kV}$ to $1 \text{ MV}$) is applied between the cathode and anode to accelerate the electrons.

  • Cooling System: Oil or water circulation to dissipate the vast amount of heat produced.

  • Vacuum: The tube is highly evacuated to prevent electrons from losing energy by colliding with air molecules.

• Energy Changes:

  1. Electrical Energy (from the accelerating potential $V$): $E = eV$

  2. Converted to Kinetic Energy of the electron beam: $eV = \frac{1}{2} m_e v^2$

  3. Converted to:

     • Heat (about $99.8\%$)

     • X-ray Energy (about $0.2\%$)

• Minimum Wavelength ($\lambda_{\text{min}}$): The maximum energy of an X-ray photon is equal to the kinetic energy of the electron.

  $$E_{\text{max}} = hf_{\text{max}} = \frac{hc}{\lambda_{\text{min}}} = eV$$

  Where $h$ is Planck's constant, $c$ is the speed of light, and $e$ is the electron charge.

2. Properties of X-rays

• Part of the electromagnetic spectrum (travel at $3.0 \times 10^8 \text{ m/s}$ in a vacuum).

• Travel in straight lines.

• Highly penetrating (pass through soft tissue but are absorbed by denser materials like bone and metal).

• Not deflected by electric or magnetic fields (since they have no charge).

• Ionize gases, causing them to conduct electricity.

• Cause certain substances to fluoresce (glow).

• Affect photographic film.

• Undergo diffraction (used in X-ray crystallography).

3. Hard and Soft X-rays

Feature	Hard X-rays	Soft X-rays
Wavelength	Shorter $\lambda$	Longer $\lambda$
Frequency/Energy	Higher $f$/Energy	Lower $f$/Energy
Penetration	High (penetrates bone/metal)	Low (only penetrates soft tissue)
Control Factor	Produced by High Accelerating Voltage	Produced by Low Accelerating Voltage

4. Factors Controlling X-ray Output

• Intensity/Quantity of X-rays: Controlled by the filament current (heating the cathode). Higher current means more electrons emitted, leading to more X-rays produced.

• Penetrating Power/Quality of X-rays (Hardness): Controlled by the accelerating potential difference ($V$). Higher voltage gives electrons more kinetic energy, producing higher frequency/shorter wavelength (harder) X-rays.

5. Uses and Dangers

Category	Uses	Dangers & Precautions
Medicine	* Radiography: Imaging bones (fractures, etc.). * Radiotherapy: Treating cancer (destroying malignant cells).	* Destroy or damage living cells. * Can cause genetic mutations from excessive exposure. * Precautions: Lead shields, limited exposure time, and dosimeters for operators.
Industry	* Checking for flaws/cracks in metal castings and welded joints. * Security (checking luggage at airports).
Science	* X-ray Crystallography: Determining the structure of crystals and complex molecules (like DNA).