By I. E Irodov

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8: For a metal at 0 K whose free electrons can reach the highest velocIty Vm, find the mean values of: (a) the velocity of free electrons; (b) the reciprocal of their velocity, 1/v. 9. 10 cm- . 10. Using a simple cubic lattice as an example demonstrate that, ~f one free electron corresponds to each atom, the shortest de B:oglle wavelength of such electrons is approximately double the dIstance between the neighbouring atoms. 11. Derive the function defining the distribution of free electrons over the de Broglie wavelengths in a metal at 0 K.

Find also the angle at which these X-rays form the highest order reflections from the given set of planes. 14. AN aCI single crystal (see Fig. 25) is photographed by Laue's method along the four-fold axis (z axis). The photoplate is located at a distance L = 50 mm from the crystal. Find for the maxima corresponding to reflections from the planes (031) and (221): (a) their distances from the centre of Laue's diagram; (b) the wavelengths of X-rays. 15. A beam of X-rays of wavelength A falls on a N aCI crystal (see Fig.

22. An A 1 radionuclide produced at the constant rate q nuclei per second goes through the following transformation chain: Ai ~ Az ~ A 3 (stable) A, A, (the decay constants are indicated under the arrows). Find the law describing the accumulation of nuclei A 1 , A 2' and A 3 in the course of time, assuming that at the initial moment the preparation did not contain any of them. 23. 1010 nuclei per second, goes through the following transformation chain 13 8Xe ------J> i38es - - - ? i38Ba (stable) 17 min 32 min (the corresponding half-lives are indicated under the arrows).