X-ray spectra | Quantum mechanics | Atomic and Molecular Physics

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.

Properties of X-rays

• 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.

X-ray spectra

• 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 below:
• 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.
• A line spectra gives the information about the target nuclei.
• Thus the spectrum from an X-ray tube contains two parts:

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.

Characteristic or line spectra

• 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.

Continuous X-ray spectrum

• 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
• The total power is directly proportional to the atomic number of target (Z).
• P ∝ Z
• ∴  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
• 𝛎_max ∝ V
• 𝛎_max = kV

Origin of continuous X-ray spectrum

Duane and Hunt’s law

• 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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