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Describe the Importance of Moseley’s Work
Characteristic X-ray Spectrum
The two sharp peaks in the spectrum of characteristic X-ray are named as Kα and Kβ. These two peaks mainly form the spectrum of the characteristic X-rays of molybdenum.
In X-ray tube (Coolidge tube), the target is bombarded by high energy cathode rays. The electrons present in the rays being of very high energy, their effect is not limited to the outer electron levels; the levels K, L, …… adjacent to the nucleus are also affected. If an electron from any of these levels comes out of the atom, a deficit of electron occurs in that orbit. If this deficit occurs in the K-orbit (the orbit closest to the nucleus), an electron from a higher energy state will transit to this K-orbit.
Now, during the transition of an electron from L -orbit to K -orbit, it radiates energy as a photon. This radiation forms the Kα -peak of the characteristic X-ray spectrum of molybdenum.
The energy level diagram of molybdenum is shown in Fig. How different peaks of the spectrum are formed has been shown in this diagram. Again, during the transition of electron from M -orbit to K -orbit, the radiation thus emitted forms the Kβ -peak of the spectrum.
This spectrum contains several smaller peaks and the brightness of these lines in the spectrum is very low. Formation of Lα and Lβ peaks among the small peaks, is also shown in Fig.
Moseley’s Law
In 1913, British physicist H. G. J. Moseley analysed the spectrum of characteristic X-rays of all the elements he knew as targets. He observed that the spectra of different elements, particularly the Kα -peaks follow a particular rule. According to the position of different elements in the periodic table, he drew a graph of the square root of the frequency of Kα and obtained a straight line.
A part of the graph is shown in Fig., on the basis of which, Moseley came to the conclusion that, “there was a fundamental quantity which increase by regular steps as we pass from one element to the next”. in 1920 Rutherford identified this quantity as the atomic number Z of the element which denotes the number of positive charges present in the nucleus. So, only from the atomic number of an element can its identity be known, not from its atomic weight.
Statement of Moseleys law: The square root of the frequency of a peak of the characteristic X-ray spectrum of any element is directly proportional to the atomic number of that element.
If the frequency of Kα -line of any element having atomic number Z be f. Then according to Moseley’s law,
\(\sqrt{f}\) ∝ Z
Explanation of Moseley’s plot from Bohr’s theory: With the help of the equation of the n-th energy state of an atom obtained from Bohr’s theory, this plot can be explained.
Equation (13) in section 1.2.3 is,
En = –\(\frac{R c h}{n^2}\) = –\(\frac{13.6}{n^2}\) eV ….. (1)
where, n = 1, 2, 3,…….
We know that in an atom containing two or more electrons only two are in the K -orbit. Let any of these come out of the atom. Then the electrons present in other orbits like L, M, ……. would experience not only the effect of positive charge of the nucleus but also the influence of the negative charges of the remaining electron in the K -orbit. This is due to the fact that, the radius of the K -orbit in an atom is the least compared to that of other orbits, So, we can assume that, relative to the surface of the sphere on which the electron of the K -orbit lies, the other electrons lie outside.
So, the effective amount of positive charge which attracts an electron of L, M, ….. orbits is (Z – 1)e, where Z is the atomic number. The above equation (1) is applicable for hydrogen atom. In case of an atom having atomic number Z, its changed form is applicable. The equation for the n-th energy-state of the atom is,
En = –\(\frac{13.6(Z-1)^2}{n^2}\)(in eV) ….. (2)
Earlier discussion shows that, Kα of the spectrum is produced due to the transition of an electron from L(n = 2) orbit to K(n = 1) orbit. Due to this transition, if the frequency of the emitted X-ray be f then
hf = (En)n = 1 = E2 – E1
= –\(\frac{13.6(Z-1)^2}{2^2}\) + \(\frac{13.6(Z-1)^2}{1^2}\)(in eV)
∴ hf = 10.2(Z – 1)2
∴ \(\sqrt{f}\) ∝ (Z – 1) ….. (3)
Equation (3) is the equation o a straight line. Hence, the graph of the square root of the frequency of the peak Ka with respect to the atomic number of the atom is a straight line. In this way, the theoretical basis of the Moseley’s plot is established in the light of Bohr’s theory.
Importance of Moseley’s work:
i) According to Moseley’s law, the characteristic X-ray spectrum is regarded as the identifying character of an element.
ii) Before 1913, the elements were arranged in the periodic table according to the increasing order of their atomic weights. In spite of that, according to the basis of chemical tests, some elements were placed before the elements having comparatively less atomic weights in the periodic table.
The reason of this exception was not understood before Moseley’s analysis. Moseley showed that, there would not be any exception to the arrangements of the periodic table, if we arranged the elements according to their increasing atomic numbers.
iii) There were many vacant places in the periodic table in 1913. After the discovery of Mosley’s law, it has been possible to fill those gaps accurately.
iv) Lanthanide elements are more or less identical in respect of their chemical properties. Thus, it was difficult to identify and to place them in the periodic table accurately. But after the discovery of Moseley’s law, it was possible to do that.
v) With the help of this plot, it was possible to identify some elements having atomic number more than that of uranium.
With the help of the visible light spectrum of an element, its atomic number cannot be determined because visible light spectrum is formed due to transition of elétrons of the outer most orbit of that atom. Now, nucleus lies at the centre of the atom. The electrons in the inner orbits cover the nucleus like a screen and hence the electrons at the outermost orbit can not give any information about the nucleus.