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Since in accord with the principle of duality no experiment can differentiate between the wave and particle predictions, it follows that the particle velocity is equal to the group velocity. 1), œ = h2k2 E = — + const. 13) that the phase velocity of the wave is a function of the wave number k: fPh = ^ - f c + ^ - . 2m nk (3-16) This means that the waves composing the group have different phase velocities, with the result that the group will change shape 46 ELECTRON THEORY OF SOLIDS with time. This type of motion is called dispersive motion, and can be inferred from the Uncertainty Principle, since if the wave group did not increase its length in time, a subsequent measure­ ment of its position would provide more accurate information than is allowed by the principle.

13) that the phase velocity of the wave is a function of the wave number k: fPh = ^ - f c + ^ - . 2m nk (3-16) This means that the waves composing the group have different phase velocities, with the result that the group will change shape 46 ELECTRON THEORY OF SOLIDS with time. This type of motion is called dispersive motion, and can be inferred from the Uncertainty Principle, since if the wave group did not increase its length in time, a subsequent measure­ ment of its position would provide more accurate information than is allowed by the principle.

In accord with the theory of Bohr, these results can be explained by attributing the X-ray emission to the rejection of a tightly bound electron from the atom by collision with the bombarding electron, followed by an electron from a less tightly bound state falling into the vacant state, with the emission of a quantum. The ATOMIC SPECTRA 33 X-ray spectrum is characteristic of the element, and is un­ affected by chemical binding, confirming that the electrons taking part in the X-ray emission process are not involved in chemical combination.

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