Energy of the x-rays are energy possessed by x-rays radiations. X -rays are electromagnetic waves of very short wavelengths of order 10-10 m. Therefore x-rays carries energies according to plank’s theory. The wavelength of the x-rays overlaps with that ultraviolet and gamma rays in electromagnetic spectrum. This is because X-rays are classified in the range 10-11 to 10-8 in electromagnetic spectrum.
Determining Energy of the x-rays
If a bombarding electron is stopped in a single collision, some or all it’s energy is converted to X-ray energy. At a given accelerating potential difference, the X-rays produced will have varying wavelengths . The minimum wavelength (λmin) corresponds with a collision in which all the kinetic energy in the motion is converted to x-rays.
The kinetic energy (K.E) of the bombarding electron is practically equal to eV. This energy is expressed as. K.E = ev where V is the accelerating potential and e the charge on an electron.
When all the kinetic energy of an electron is used to produce x-ray waves, the frequency of the x-rays produced will be maximum. This maximum frequency is expressed as fmax.
Using Plank’s theory, the X-ray energy is given by: E= hf. where h is the Plank’s constant and f the frequency of the radiation.
eV = hfmax
remember that speed of a wave is given by the general equation v=fλ. But x-rays being part of electromagnetic spectrum moves at a speed of light represented by c.
Hence the speed of the x-ray waves will be c= fλ, c being the speed of light.(c=3.0 x 108 ms-1)
Therefore the speed of the x-ray waves produced will be given by: c = fmaxλmin.
we now express frequency of the x-ray produced in terms of speed and wavelength:
Therefore:
From the equation, we see that the most energetic X-rays have the shortest wavelength.
Example problem on energy of the x-rays
Find the frequency and the energy of a type of X-rays whose wavelength is 10-10 m. (velocity of light c = 3.0 x 108 ms-1, Plank’s constant h = 6.63 x 10-34 Js).
solution
c=fλ
E=hf
E = 6.63 x 10-34 x 3.0 x 1018 = 1.989 x 10-15J
practice Questions
1. The frequency of X-rays ranges from 3.0 x 1017 to 3.0 x 1019Hz. Determine
(a) the range of the wavelengths.
(b) the maximum energy of the X-rays. (velocity of light c= 3.0 x 108ms-1 and plank’s constant h= 6.63 x 10-34Js)
2. An X-ray tube has an accelerating potential difference of 100 Kv. what is the shortest wavelength in its X-beam? Take plank’s constant h=6.63 x 10-34Js, charge on an electron e = 1.6 x 10-19C and velocity of light c = 3.0 x 108ms-1.
hard x-rays
X-rays are usually classified as hard or soft. Hard x-rays are described as having high frequency hence shorter wavelengths and so high penetrating power. Hard X-rays are produced by use of high accelerating voltage that causes the electrons move at very high speed towards the target in the x-ray tube.
soft x-rays
Soft X-rays are produced by electrons moving at relatively lower velocities . They are of less energy and lower frequency. Specifically, they fall within the 100-3,000 eV energy range. Due to their lower energy, soft X-rays are more readily absorbed by matter and have limited penetrating power, requiring measurements to be conducted in a vacuum. They are valuable for studying surfaces, near-surface interfaces, and for spectroscopic techniques like X-ray Absorption Spectroscopy (XAS) and X-ray Photoelectron Spectroscopy (XPS)