X-ray spectra

X-rays

X-rays were discovered by a German physicist Wihelm Conrad Roentgen in 1895 during the study of the properties of cathode rays.
These rays are actually electromagnetic rays of lower wavelengths having range from 10 Å to 0.5 Å.
Higher wavelength side X-rays are soft X-ray and the lower wavelength side X-rays are hard X-ray.

Since the X-rays do not deflect by electric and magnetic fields, hence they does not consist of charged particles.
X-rays are electromagnetic radiation of very short wavelength.
X-rays affect photographic plate like light, but their effect is much more intense than light.

X-rays travel in straight lines with the velocity of light.
They produce fluorescence in several materials.
X-rays ionize the gas through which they pass.
X-rays have high penetrating power and can pass through many solids.
They produce photo electric effect also.
X-rays also show interference, diffraction and polarization similar to the light rays.

The wavelength of X-rays can be determined by Bragg’s law.
If we plot a graph between wavelength of X-rays obtained from any source and their intensity then the graph will be according to figure given above.
Three waves are shown using Rh (Rhodium) as a target and at different potential differences.
It is clear from spectrum that at every stage, spectrum is continuous and obtained at a particular wavelength.
If applied potential difference is below 23 kV, then only continuous emission spectra is obtained.
But at higher potential difference a line spectrum is also overlapped with a continuous spectrum.

It consists of all possible wavelengths, from a certain lower limit to higher values continuously, like a visible spectrum. So it is also known as white spectrum.

It consists of definite well defined wavelengths superimposed on the continuous spectrum.
The spectral lines of this spectrum generally occurs in small groups.
These lines are characteristics of the material of the target nuclei.

The continuous X-ray spectrum was discovered by Duane and Hunt.
If by taking tungsten element as a target nuclei and by applying different potential difference on the X-ray tube, we plot the intensities of the rays produced against wavelength, then the curve will be according to the figure.

This curve provide the continuous X-ray spectra.
For each potential difference the intensity-wavelength (I-λ) curve starts at a particular wavelength, rises rapidly to a maximum and then drops gradually.
The wavelength at which the intensity become maximum depends on accelerating voltage (V_a). Higher the value of accelerating voltage, higher will be the intensity.
The peak intensity shift towards the shorter λ side as the value of V_a increases. Thus the penetration power of X-rays increases with the voltage.
For each anode potential, there is a minimum wavelength (λ_min) below which no radiation is emitted. Its value depends on the target nuclei and above this critical value, the intensity of radiation increases.
By applying different potential difference at X-ray tube, we get continuous spectrum for every wavelength.
The total power of X-rays (P) depends on the area of experimental wave.
The total power is directly proportional to the square of the applied voltage.

P ∝ V²

P ∝ Z

or P ∝ ZV²⇒ P = kZV²

Here k is proportionality constant
When the voltage across the X-ray tube is increased, λ_min shifted towards small value.

∴ λ_min ∝ 1/V

or ν_max ∝ V
or ν_max = kV

If a high energy electron beam incident on a target nuclei, then it enters into the target and deviates from its actual path.
In this process the loss of energy of incident electron beam provides an X-ray photon and electron loses its velocity due to interaction with strong field of target.

If u₁ and u₂ be the initial and final velocities of electron, then
Energy of X-ray photon, hν = ½ mu₁² − ½ mu₂²
If electron stops into the target, then u₂ = 0, ν = ν_max
hν = mu₁²
eV = hν_max
eV = ch / λ_min (∵ c = νλ)
λ_min = ch / eV
This is Duane and Hunt’s law.
λ_min = (12400 / V) Å
Most of the electron that generate X-ray photon give up only a part of their energy in this process.
Therefore most of the X-radiation is of longer wavelength than λ_min.
Thus continuous spectrum is the result of the inverse photo electric effect.

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