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Atoms — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsAtoms5 Marks
Question
Explain characteristic X-rays. Calculate minimum wavelength of X-rays emitted from X-ray tube operating at 5 kV.
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Answer

Characteristic X-rays : When the continuous spectrum was examined with Bragg's spectrometer precisely, some sharp peaks were observed in intensity-wavelength curve. The reason for these peaks are some characteristic wavelengths found in continuous spectrum of X-rays and these are the characteristics of the material of the target. The X-rays corresponding to these particular wavelengths are called characteristic X-rays. [Fig. (a)] Most of the elements show in their X-ray spectra two series of lines, known as K-series and L-series. Each series contains a small number of lines designated as $K _\alpha, K _\beta, \ldots \ldots$,$L _\alpha, L _\beta \ldots \ldots .$.The wavelengths of K-series are generally less than 1 Å, while those of L-series are roughly ten times larger. Heavier elements (Z > 66) show further series known as M-, N-, O- series.
Kossel explained the origin of the characteristic X-ray line spectrum on the basis of the shell structure of the atom. An atom is built up of a central positively-charged nucleus with discrete aggregates of electrons, known as K-shell, L-shell, M-shell, N-shell, etc. The maximum number of electrons which the K, L, M, N,......... shells can hold are 2, 8, 18, 32, The electrons in the K-shell are attracted by the positive nucleus with the greatest force, and to eject them from the atom maximum energy is required. Less energy is required to eject an electron from the L-shell, still less from M-shell, and so on.
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Now, in an X-ray tube an electron emitted from the cathode strikes the target with a tremendous velocity so that it penetrates well inside the atoms of the target. If it ejects an electron from the K-shell of the atom, a vacancy is created in the K-shell. Immediately an electron from one of the outer shells, say L-shell jumps to the K-shell, emitting an X-ray photon of energy equal to the difference in the binding energies of the electron in the K and L shells. Similarly, if an electron from the M-shell jumps to the K-shell, X-ray photon of higher energy is emitted. The X-ray photons emitted due to the jump of electrons from the L, M, N, ..... shell to the K-shell give $K _\alpha, K _\beta, K _\gamma \ldots \ldots$ lines of the K-series of the spectrum.
Energy Level Diagram : The formation of spectral series of characteristic X-rays on an energy level diagram is shown in Fig. (b). In X-ray energy levels zero energy level is assigned to the normal state of the atom.
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If one of the most firmly bound electrons of the K-shell is removed, the atom is said to be in K-level. An electron from any one of the outer levels L, M, N,...... then falls into the K-level with the emission of a K-series line. Similarly, the formation of other series lines can be explained.
First, second, third, line of each series is assigned the subscript $\alpha, \beta, \gamma, \ldots \ldots$. respectively [Fig. (b)].
Solution of Numerical : Minimum Wavelength of X-ray :
$\lambda_{\min }=\frac{h c}{e V}=\left[\frac{\left(6.6 \times 10^{-34}\right)\left(3 \times 10^8\right)}{\left(1.6 \times 10^{-19}\right)\left(5 \times 10^3\right)}\right] m$
$=2.475 \times 10^{-10} m$ = 2.475 Å

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