X-Ray Tube (OCR A Level Physics)

• An X-ray tube is a device that converts an electrical input into X-rays
• It is composed of four main components:
  • A heated cathode
  • An anode
  • A metal target
  • A high voltage power supply

• The production of X-rays has many practical uses, such as in:
  • Medical imaging (radiography)
  • Security
  • Industrial imaging

The main components of an X-ray Tube are the heated cathode, anode, metal target and a high voltage supply

The Role of the Components

Heated Cathode

• At one end of the tube is the cathode (negative terminal) which is heated by an electric current
  • The heat causes electrons to be liberated from the cathode, gathering in a cloud near its surface
  • This process of thermionic emission is the source of the electrons 

Anode

• At the other end of the tube, an anode (positive terminal) is connected to the high voltage supply
• This allows the electrons to be accelerated up to a voltage of 200 kV 
  • When the electron arrives at the anode, its kinetic energy is 200 keV (by the definition of an electronvolt)
• Only about 1% of the kinetic energy is converted to X-rays
  • The rest is converted to heat energy
  • Therefore, to avoid overheating, the anode is spun at 3000 rpm and sometimes water-cooled

Metal Target

• When the electrons hit the target at high speed, they lose some of their kinetic energy
  • This is emitted as X-ray photons
• A heat-resistant block of metal, usually Tungsten, is embedded at the end of the anode, facing the cathode
  • This is the material that the electrons collide with and X-rays are generated in

High Voltage Power Supply

• The high voltage supply creates a large potential difference (> 50 kV) between the cathode and the target
  • This causes electrons in the cloud around the cathode to be accelerated to a high velocity towards the target, which they strike, creating X-rays

Other Components

• X-rays are produced in all directions, so the tube is surrounded by lead shielding
  • This is to ensure the safety of the operators and recipients of the X-rays
  • An adjustable window allows a concentrated beam of X-rays to escape and be controlled safely
• The anode and cathode are housed inside a vacuum chamber
  • This is to ensure that the electrons do not collide with any particles on their way to the metal target

• When the fast-moving electrons collide with the target, X-rays are produced by one of two methods
  • Method 1: Bremsstrahlung
  • Method 2: Characteristic Radiation

Method 1: Bremsstrahlung

• When the high-speed electrons collide with the metal target, they undergo a steep deceleration
  • When a charged particle decelerates quickly, some of the energy released is converted into a photon
• A small amount of the kinetic energy (~ 1%) from the incoming electrons is converted into X-rays as the electrons decelerate in the tungsten, due to conservation of energy 
  • The rest of the energy heats up the anode, which usually requires some form of cooling
• The energy of the X-ray photon can be of any value, up to the original kinetic energy of the electron, giving a spread of possible X-ray energies
  • These X-rays cause the continuous or ‘smooth hump shaped’ line on an intensity wavelength graph

• When an electron is accelerated, it gains energy equal to the electronvolt, this energy can be calculated using:

E_max = eV

• This is the maximum energy that an X-ray photon can have
• The smallest possible wavelength is equivalent to the highest possible frequency and therefore, the highest possible energy
  • This is assuming all of the electron’s kinetic energy has turned into electromagnetic energy

• Therefore, the maximum X-ray frequency f_max, or the minimum wavelength λ_min, that can be produced is calculated using the equation:

• The maximum X-ray frequency, f_max, is therefore equal to:

• The minimum X-ray wavelength, λ_min, is therefore equal to:

• Where:
  • e = elementary charge (C)
  • V = potential difference between the anode and cathode (V)
  • h = Planck's constant (J s)
  • c = the speed of light (m s⁻¹)

Method 2: Characteristic Radiation

• Some of the incoming fast electrons cause inner shell electrons of the tungsten to be ‘knocked out’ of the atom, leaving a vacancy
  • This vacancy is filled by an outer electron moving down and releasing an X-ray photon as it does (equal in energy to the difference between the two energy levels)
  • Because these X-rays are caused by energy level transitions, they have only specific discrete energies
  • They cause sharp spikes on an intensity wavelength graph
  • The number of spikes depends on the element used for the target - there are two sets of spikes for a tungsten target, representing two sets of possible energy transitions

Step 1: Write out known quantities

• • Charge on an electron, e = 1.6 × 10⁻¹⁹ C
  • Accelerating potential difference, V = 60 000 V
  • Planck’s constant, h = 6.63 × 10⁻³⁴ J s
  • Speed of light, c = 3 × 10⁸ m s⁻¹

Step 2: Determine the maximum possible energy of a photon

• • The maximum possible energy of a photon corresponds to the maximum energy an electron could have:

E_max = eV

Step 3: Determine an expression for minimum wavelength

Planck relation:    E = hf

Wave equation:    c = fλ

• • When energy is a maximum:

E_max = eV = hf_max

• • Maximum energy corresponds to a minimum wavelength:

• • Rearrange for minimum wavelength, λ_min:

Step 4: Calculate the minimum wavelength λ_min

λ_min = 2.1 × 10⁻¹¹ m

Step 5: Comment on whether this is within the range for the wavelength of an X-ray 

• • X-ray wavelengths are within 10⁻⁸ to 10⁻¹³ m
  • The minimum wavelength for a 60 kV supply is 2.1 × 10⁻¹¹ m, which means the photons produced will be X-rays

Part (a)

Step 1: Consider the path of the electrons from the cathode to the anode

• • Photons are produced whenever a charged particle undergoes a large acceleration or deceleration
  • X-ray tubes fire high-speed electrons at a metal target
  • When an electron collides with the metal target, it loses energy in the form of an X-ray photon as it decelerates

Step 2: Consider the relationship between the energy of the electron and the wavelength of the photon

• • The wavelength of a photon depends on the energy transferred by a decelerating electron
  • The electrons don't all undergo the same deceleration when they strike the target
  • This leads to a distribution of energies, hence, a range, or continuous spectrum, of wavelengths is observed

Part (b)

Step 1: Identify the significance of the intensity 

• • The intensity of the graph signifies the proportion of photons produced with a specific energy, or wavelength
  • The higher the intensity, the more photons of a particular wavelength are produced
  • In other words, the total intensity is the sum of all the photons with a particular wavelength

Step 2: Explain the shape of the graph

• • When a single electron collides with the metal target, a single photon is produced
  • Most electrons only give up part of their energy, and hence there are more X-rays produced 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)

Step 1: Identify the relationship between minimum wavelength and maximum energy

• • The minimum wavelength of an X-ray is equal to

• • The equation shows the maximum energy of the electron corresponds to the minimum wavelength, they are inversely proportional 

• • Therefore, the higher the energy of the electron, the shorter the wavelength of the X-ray produced

Step 2: Explain the presence of the cut-off point

• • The accelerating voltage determines the kinetic energy which the electrons have before striking the target
  • The value of this accelerating voltage, therefore, determines the value of the maximum energy
  • This corresponds to the minimum, or cut-off, wavelength