X-Ray Production

X-Ray Production Overview

  • X-ray radiation is produced in X-ray emission tubes by colliding high-energy electrons with metal atoms.

Types of X-Rays

  • Characteristic X-rays

    • Produced when incoming electrons knock out electrons from inner shells of atoms.

    • An electron is ejected from a lower energy shell, leaving a vacancy.

    • An electron from a higher energy level drops down to fill this vacancy, releasing energy as an X-ray.

    • The energy of the emitted X-ray corresponds to the difference in energy levels.

  • Bremsstrahlung (German for "breaking radiation")

    • Unlike characteristic X-rays, electrons are not knocked out; instead, they decelerate as they pass near the nucleus, causing a change in direction and velocity.

    • The energy lost due to this deceleration is emitted as an X-ray.

    • The amount of energy (and thus the wavelength) of the X-ray depends on how much the electron is slowed down.

Characteristic X-Ray Details

  • Frequency is determined by the change in quantum states of the electrons in the atom.

  • Emission occurs at specific energy levels, leading to sharp spikes in intensity on a spectra graph.

Bremsstrahlung X-Ray Details

  • Emitted continuously rather than at distinct frequencies, resulting in a broader spectrum of wavelengths.

  • Energy distribution is continuous; the maximum energy corresponds to the minimum wavelength, associated with full conversion of kinetic energy of the electron into X-ray energy.

  • The intensity of bremsstrahlung radiation is generally larger in total energy than that of characteristic X-rays despite having lower peak intensities.

Key Equations

  • Relation between energy and frequency: [ E = hf ]

  • The maximum frequency of an emitted X-ray is calculated by dividing the kinetic energy of an electron by Planck's constant, yielding [ f_{max} = \frac{E_{kinetic}}{h} ]

  • Wavelength relation: [ E = \frac{hc}{\lambda} ] with rearrangement leading to [ \lambda_{min} = \frac{hc}{E} ]

Examples and Calculations

  1. Maximum frequency from kinetic energy

  • For 75,000 eV energy, calculated frequency: [ f_{max} = 1.8 \times 10^{19} Hz ]

  • This frequency is within the X-ray spectrum of 10^16 to 10^19 Hz.

  1. Wavelength calculation for electron energy

  • For 500 eV kinetic energy from a potential difference: [ \lambda = 2.5 \times 10^{-9} m ] (2.5 nm)

  1. Energy level transitions

  • From energy levels n=3 to n=1, energy difference: 19.5 kilo-electron volts leads to frequency calculation of 4.7 \times 10^{18} Hz.