When electrons with an energy of 80 keV strike a tungsten target in an X-ray tube, several interactions can occur, leading to the emission of X-rays. To determine the correct answer from the options provided, we need to analyze the processes involved in X-ray production and the energy levels of the tungsten atoms.
Understanding X-ray Production
In an X-ray tube, high-energy electrons collide with a metal target, such as tungsten. This collision can result in two primary types of X-rays:
- Bremsstrahlung Radiation: This is a continuous spectrum of X-rays produced when electrons are decelerated upon interaction with the electric fields of the tungsten nuclei. The energy of these X-rays can vary, leading to a range of wavelengths.
- Characteristic X-rays: When an incident electron has enough energy to knock out an inner-shell electron (like a K-shell electron) from the tungsten atom, an electron from a higher energy level will fall into this vacancy. The energy difference between these two levels is emitted as a photon, resulting in X-rays with specific wavelengths characteristic of tungsten.
Analyzing the Given Energies
The K-shell electrons of tungsten have an energy of -72.5 keV. This means that to remove a K-shell electron, an incident electron must have at least 72.5 keV of energy. Since the incident electrons have 80 keV, they have sufficient energy to eject K-shell electrons and produce characteristic X-rays.
Minimum Wavelength Calculation
The minimum wavelength of the emitted X-rays can be calculated using the formula:
λ = (hc) / E
Where:
- λ = wavelength
- h = Planck's constant (approximately 4.1357 x 10-15 eV·s)
- c = speed of light (approximately 3 x 108 m/s)
- E = energy of the incident electrons (80 keV)
Converting 80 keV to joules (1 eV = 1.6 x 10-19 J), we find:
E = 80,000 eV = 80,000 x 1.6 x 10-19 J
Now, substituting the values into the wavelength formula gives us the minimum wavelength, which can be calculated to be approximately 0.155 Å (angstroms).
Conclusion on X-ray Emission
Given that the incident electrons can produce both Bremsstrahlung radiation (which includes a continuous spectrum with a minimum wavelength) and characteristic X-rays (due to the ejection of K-shell electrons), the correct answer to the question is:
d) A continuous X-ray spectrum (Bremsstrahlung) with a minimum wavelength of 0.155 Å and the characteristic X-ray spectrum of tungsten.
This option encompasses both types of X-rays produced during the interaction, making it the most comprehensive choice. The continuous spectrum arises from the deceleration of electrons, while the characteristic spectrum results from transitions of electrons within the tungsten atoms.
