Continuous x-ray spectra:
When a fast moving electron penetrates and approaches a target nucleus, the interaction between the electron and the nucleus either accelerates or decelerates it which results in a change of path of the electron. The radiation produced from such decelerating electron is called Bremsstrahlung or braking radiation
The energy of the photon emitted is equal to the loss of kinetic energy of the electron. Since an electron may lose part or all of its energy to the photon, the photons are emitted with all possible energies (or frequencies). The continuous x-ray spectrum is due to such radiations.
When an electron gives up all its energy, then the photon is emitted with highest frequency υ (or lowest wavelength λ ). The initial kinetic energy of an electron is given by eV where V is the accelerating voltage. Therefore, we have
hυ0 = eV (or) = \(\frac{hc}{λ_0}\) =ev
λ0 = \(\frac{hc}{eV}\)
where λ0 is the cut-off wavelength. Substituting the known values in the above equation, we get
λ0 = \(\frac{122400}{V}\) Å
The relation given by equation is known as the Duane – Hunt formula.
The value of λ depends only on the accelerating potential and is same for all targets. This is in good agreement with the experimental results. Thus, the production of continuous x-ray spectrum and the origin of cut – off wavelength can be explained on the basis of photon theory of radiation.
