X-Ray Production and Spectra

Overview

X-rays are high-frequency electromagnetic waves with very short wavelengths and high photon energies.

They are commonly produced when fast-moving electrons strike a metal target.

This topic is part of Quantum Physics because it combines:

• electron acceleration
• photon production
• quantised atomic energy levels
• spectral interpretation

Definition

X-rays are electromagnetic radiation produced in X-ray tubes mainly by rapid electron deceleration and by inner-shell electronic transitions in target atoms.

Why It Matters

This topic explains:

• how electrical energy is converted into high-energy photons
• why X-ray spectra have both continuous and discrete parts
• how voltage, current, and target material affect the output

Key Representations

Properties of X-Rays

X-rays:

• are electromagnetic waves
• travel at speed $c$ in vacuum
• have short wavelengths
• have high frequencies
• are ionising radiation
• are highly penetrating

Applications include:

• medical imaging
• material testing
• crystallography

X-Ray Tube Setup

A typical X-ray tube contains:

• heated filament, the cathode
• metal target, the anode
• evacuated tube
• high accelerating voltage
• cooling system

Process:

1. the filament emits electrons by thermionic emission
2. electrons accelerate through potential difference $V$
3. electrons strike the metal target
4. part of their energy becomes X-rays

Most energy becomes heat.

Electron Acceleration

Each electron gains kinetic energy:

$$KE=eV$$

where:

• $e$ = elementary charge
• $V$ = accelerating voltage

Higher voltage gives higher electron kinetic energy.

How X-Rays Are Produced

When electrons strike target atoms, they may:

• decelerate rapidly near nuclei
• eject inner-shell electrons
• cause electron transitions inside target atoms

These processes generate two spectral components.

X-Ray Spectrum Components

A typical X-ray spectrum contains:

1. continuous spectrum
2. characteristic lines

Continuous X-Ray Spectrum

Also called Bremsstrahlung, braking radiation.

Produced when incident electrons are decelerated by target nuclei.

Why continuous:

Electrons may lose different amounts of energy in different collisions.

Therefore emitted photons can have a range of energies.

This gives a smooth background spectrum.

Characteristic X-Ray Lines

Sharp peaks superimposed on the continuous spectrum.

Produced when:

1. an incident electron ejects an inner-shell electron
2. a vacancy is created
3. a higher-level electron falls to a lower level
4. a photon is emitted with specific energy

Thus:

$$hf=\Delta E$$

These energies depend on the target material.

Minimum Wavelength

Maximum possible photon energy occurs when one electron loses all its kinetic energy in a single interaction.

Then:

$$eV=hf=\frac{hc}{{\lambda }_{\min }}$$

Hence:

$${\lambda }_{\min }=\frac{hc}{eV}$$

Meaning of Minimum Wavelength

• shortest wavelength in the continuous spectrum
• highest photon energy possible
• determined by tube voltage only

Effect of Tube Voltage

Increasing $V$ causes:

1. higher electron kinetic energy
2. smaller minimum wavelength
3. greater overall intensity
4. characteristic lines may appear if voltage is high enough to eject inner-shell electrons

Effect of Tube Current

Higher tube current means:

• more electrons strike the target each second
• greater X-ray intensity

But:

• maximum photon energy is unchanged
• ${\lambda }_{\min }$ is unchanged

if voltage is constant.

Effect of Target Material

Changing target metal changes:

• characteristic-line positions
• relative intensity pattern

Because different atoms have different internal energy levels.

However:

• ${\lambda }_{\min }$ depends mainly on voltage, not target material

Spectral Interpretation

Continuous background:

• from electron deceleration

Sharp peaks:

• from atomic transitions in target atoms

Cut-off at short-wavelength end:

• marks ${\lambda }_{\min }$

Summary

X-rays are produced when fast electrons hit a metal target.

Two components:

• continuous Bremsstrahlung spectrum
• characteristic lines

Key equation:

$$eV=hf=\frac{hc}{{\lambda }_{\min }}$$

Important ideas:

• voltage controls maximum photon energy
• current controls intensity
• target material controls characteristic lines

Links

• Quantum Physics
• Atomic Structure
• Photoelectric Effect
• Quantum Physics Common Exam Traps