# X-Ray Tube ## Structure of an X-ray Tube - An X-ray tube converts electrical energy into X-rays - It consists of four key components: - A heated cathode - An anode - A metal target - A high voltage power supply - X-ray production has many applications: - Medical imaging (radiography) - Security screening - Industrial imaging

An X-ray tube is a device that transforms electrical input into X-ray photons through electron bombardment of a metal target

## Component Functions ### Heated Cathode - Located at one end of the tube as the negative terminal - Heated by passing an electric current through it - The heating liberates electrons from the cathode surface, forming an electron cloud nearby - This process of **thermionic emission** provides the source of electrons for X-ray production ### Anode - Positioned at the opposite end of the tube as the positive terminal - Connected to a high voltage power supply - Accelerates electrons to voltages up to 200 kV - When an electron reaches the anode, its kinetic energy equals 200 keV (by definition of the electronvolt) - Only approximately 1% of electron kinetic energy converts to X-rays - The remaining 99% transforms into heat energy - To prevent overheating: - The anode rotates at 3000 rpm - Water-cooling is sometimes employed ### Metal Target - A heat-resistant metal block, typically tungsten, embedded at the anode end facing the cathode - High-speed electrons collide with this target material - During collision, electrons lose kinetic energy - This lost energy is emitted as X-ray photons ### High Voltage Power Supply - Creates a large potential difference (exceeding 50 kV) between cathode and target - Electrons in the cathode cloud are accelerated to high velocities - High-velocity electrons strike the target, generating X-rays ## Additional Components ### Lead Shielding - X-rays are emitted in all directions from the target - The entire tube is surrounded by lead shielding - Ensures safety of operators and patients - An adjustable window permits a controlled, concentrated X-ray beam to escape ### Vacuum Chamber - Houses both the anode and cathode - Ensures electrons travel unimpeded to the metal target - Prevents collisions with air particles that would reduce electron energy ## Production of X-ray Photons - When fast-moving electrons collide with the target, X-rays are produced by two distinct mechanisms: - Method 1: Bremsstrahlung - Method 2: Characteristic Radiation ### Method 1: Bremsstrahlung - High-speed electrons undergo rapid deceleration upon hitting the metal target - When charged particles decelerate quickly, energy is released as photons - Approximately 1% of the incoming electron's kinetic energy converts to X-rays due to conservation of energy - The remaining energy heats the anode, necessitating cooling systems - The X-ray photon energy can have any value up to the original electron kinetic energy - This produces a spread of X-ray energies - These X-rays create a continuous or 'smooth hump-shaped' distribution on an intensity-wavelength graph

Bremsstrahlung (German for "braking radiation") produces a continuous spectrum because electrons lose varying amounts of energy during deceleration

### Maximum X-ray Energy - When an electron is accelerated through potential difference $V$, it gains energy: $$E_{\max} = eV$$ - This is the maximum energy an X-ray photon can possess - The smallest wavelength corresponds to the highest frequency and highest energy - This assumes all electron kinetic energy converts to electromagnetic energy ### Maximum Frequency and Minimum Wavelength - The maximum X-ray frequency $f_{\max}$ or minimum wavelength $\lambda_{\min}$ is calculated using: $$E_{\max} = eV = hf_{\max} = \frac{hc}{\lambda_{\min}}$$ - Therefore, the **maximum X-ray frequency** is: $$f_{\max} = \frac{eV}{h}$$ - And the **minimum X-ray wavelength** is: $$\lambda_{\min} = \frac{hc}{eV}$$ Where: - $e$ = elementary charge (C) - $V$ = potential difference between anode and cathode (V) - $h$ = Planck's constant (J s) - $c$ = speed of light (m s$^{-1}$) ### Method 2: Characteristic Radiation - Some incoming fast electrons knock out inner shell electrons from tungsten atoms - This creates a vacancy in the inner electron shell - An outer electron drops down to fill the vacancy - As it transitions, an X-ray photon is released - The photon energy equals the energy difference between the two levels - Because these arise from energy level transitions, they have specific discrete energies only - They produce sharp spikes on an intensity-wavelength graph - The number of spikes depends on the target element - Tungsten targets produce two sets of spikes, representing two sets of possible energy transitions

Characteristic radiation produces discrete line spectra specific to the target material, while bremsstrahlung produces a continuous spectrum

## The X-ray Spectrum The typical X-ray spectrum from a tungsten target shows both the continuous bremsstrahlung radiation and the characteristic line spectrum superimposed:

Key features of this spectrum: - **Sharp cut-off** at $\lambda_{\min}$ (0.014 nm in this example) - no X-rays produced below this wavelength - **Continuous spectrum** from bremsstrahlung - smooth curve extending to longer wavelengths - **Characteristic K$_\beta$ spike** at 0.0184 nm - higher energy transition - **Characteristic K$_\alpha$ spike** at 0.0209 nm - lower energy transition (more intense) - **Steeper gradient** at short wavelengths - fewer electrons transfer all their energy - **Peak intensity** occurs at wavelengths longer than $\lambda_{\min}$ - most electrons transfer only part of their energy ## Worked Example: Determining X-ray Wavelength Range **Question:** X-rays are electromagnetic waves with wavelengths ranging from $10^{-8}$ to $10^{-13}$ m. If the accelerating potential difference in an X-ray tube is 60 kV, determine whether the photons emitted fall within this range. **Solution:** ### Step 1: List known quantities - Charge on an electron: $e = 1.6 \times 10^{-19}$ C - Accelerating potential difference: $V = 60\,000$ V - Planck's constant: $h = 6.63 \times 10^{-34}$ J s - Speed of light: $c = 3 \times 10^{8}$ m s$^{-1}$ ### Step 2: Determine maximum photon energy The maximum photon energy equals the maximum electron energy: $$E_{\max} = eV$$ ### Step 3: Derive minimum wavelength expression From Planck relation: $E = hf$ From wave equation: $c = f\lambda$ When energy is maximum: $$E_{\max} = eV = hf_{\max}$$ Maximum energy corresponds to minimum wavelength: $$eV = \frac{hc}{\lambda_{\min}}$$ Rearranging for minimum wavelength: $$\lambda_{\min} = \frac{hc}{eV}$$ ### Step 4: Calculate minimum wavelength $$\lambda_{\min} = \frac{(6.63 \times 10^{-34})(3 \times 10^{8})}{(1.6 \times 10^{-19})(60\,000)}$$ $$\lambda_{\min} = 2.1 \times 10^{-11} \text{ m}$$ ### Step 5: Conclusion - X-ray wavelengths range from $10^{-8}$ to $10^{-13}$ m - The minimum wavelength for a 60 kV supply is $2.1 \times 10^{-11}$ m - This falls within the X-ray range, confirming the photons produced are X-rays ## Worked Example: Explaining the X-ray Spectrum **Question:** A typical spectrum of X-ray radiation produced by electron bombardment of a metal target is shown. Explain why: a) A continuous spectrum of wavelengths is produced b) The gradient is steeper at shorter wavelengths c) The spectrum has a sharp cut-off at short wavelengths **Solution:** ### Part (a): Continuous Spectrum - Photons are produced whenever charged particles undergo large acceleration or deceleration - X-ray tubes fire high-speed electrons at a metal target - When electrons collide with the target, they lose energy as X-ray photons while decelerating - The wavelength of a photon depends on the energy transferred by a decelerating electron - Electrons don't all undergo identical deceleration when striking the target - This leads to a distribution of energies - Hence, a range (or continuous spectrum) of wavelengths is observed ### Part (b): Steeper Gradient at Short Wavelengths - The intensity signifies the proportion of photons produced with a specific energy or wavelength - Higher intensity means more photons of that particular wavelength are produced - The total intensity represents the sum of all photons with a particular wavelength - When a single electron collides with the target, a single photon is produced - Most electrons transfer only part of their energy, producing more X-rays at wavelengths higher than the minimum (or energies lower than the maximum) - At short wavelengths, there is a steeper gradient because only a few electrons transfer all, or most of, their energy ### Part (c): Sharp Cut-off Point - The minimum wavelength of an X-ray equals: $$\lambda_{\min} = \frac{hc}{E_{\max}}$$ - The equation shows maximum electron energy corresponds to minimum wavelength (they are inversely proportional): $$\lambda_{\min} \propto \frac{1}{E_{\max}}$$ - Higher electron energy produces shorter wavelength X-rays - The accelerating voltage determines the electrons' kinetic energy before striking the target - This accelerating voltage value determines the maximum energy value - This corresponds to the minimum (cut-off) wavelength