By John C Morrison
Superb ebook for enthusiastic undergraduate scholars to get the fundamentals of Quantum concept from a phenomenological point of view
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Extra resources for Modern Physics for Scientists and Engineers
The transitions of these series are referred to in a manner similar to that used for the transitions in the visible part of the spectra. The ﬁrst member of the Lyman series, for instance, corresponds to the transition n = 2 → n = 1 and is referred to as Lyman-α (Lα ), and the ﬁrst member of the Paschen series corresponds to the transition n = 4 → n = 3 and is referred to as Paschen-α (Pα ). Successive members of these series are referred to as Lyman-β and Paschen-β, and so forth. 6 The energy levels of the hydrogen atom.
Setting n = 1 in eq. 19), we obtain a0 = 4π 0 2 . 529 Å. The radius of the hydrogen atom is thus equal to about a half an Angstrom. The expression for the energy in the Bohr model can be obtained by substituting eq. 19) into eq. 16) giving En = − me4 2(4π 0 )2 2 1 , n2 9 where n = 1, 2, 3, . . , and, as before, is equal to Planck’s constant divided by 2π. The energies En given by this formula can be evaluated using the table of the fundamental constants given in Appendix A. In order to obtain a simpler form of this equation for En , we rewrite it in the following way: En = − 1 2 1 e2 4π 0 a0 1 .
Using the fact that energy and momentum are conserved in collision processes, Compton derived a formula relating the wavelength λ of the scattered radiation to the wavelength λ of the incident radiation and the angle θ of the scattered radiation. 23) where h is Plank’s constant, m is the mass of the electron, and c is the velocity of light. This equation accurately describes Compton’s data and the data of subsequent experiments on the scattering of X-rays by loosely bound electrons. 9 Scattered photon Incident photon E9, p9 Q E, p Ee, pe Scattered electron The scattering of a photon with energy E and momentum p from an electron that is initially at rest.