A collection of problems in atomic and nuclear physics by I. E Irodov

By I. E Irodov

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V . • . • . 25 Find the half-lives of both components and the ratio of radioactive nuclei of these components at the moment t = O. 13. A radionuclide A 1 with decay constant A1 transforms into a radionuclide A 2 with decay constant A2. Assuming that at the initial moment the preparation consisted of only N 10 nuclei of radionuclide A 1 , find: (a) the number of nuclei of radionuclide A 2 after a time interval t; (b) the time interval after which the number of nuclei of radionuclide A 2 reaches the maximum value; (c) under what condition the transitional equilibrium state can evolve, so that the ratio of the amounts of the radionuclides remains constant.

4. f':centererl cubic lattices. 5. 5 g/cm 3 • The lattice in question is of the cubic NaCI type. 6. Determine the ratio of periods of identity along the directions [100l, [110l, and [111] for the simple, space-centered, and facecentered cubic lattices. 7. 23 A. 8. A parallel X -ray beam with the wavelength A falls in an arbitrary direction on a plane rectangular net with periods a and b. What pattern will be observed on a screen positioned parallel to the plane net? Find the directions to the diffraction maxima.

1 ) where B is the rotation constant, I is the molecule's moment of inertia, J is the rotation quantum number, J = 0, 1, 2, ... J = ±1. / f" } \ 2\ / I I \ n LJ=O "" / o quasielastic force constant, . i/ n j a r ro b Fig. 24 Fig. l is the reduced mass of a molecule,. er, vl~ =0, 1, 2, ... , x is the anharmoniClty coeffiCIent (x = 0 for harmolllc oSCIllator). v selection rule: L\v= { ±1, ±1, if x=O ±2, •.. in other cases. • Interaction energy as a function of the distance bet ween the nuclei of a diatomic molecule is shown in Fig.

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