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

By I. E Irodov

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25. Using the expression for the magnetic moment of an atom, derive the formula for spectral line splitting in the case of the anomalous Zeeman effect in a weak magnetic field. 26. What kind of the Zeeman effect, normal or anomalous, is observed in a weak magnetic field in the case of spectral lines: (a) 1p-+- 18, 2D 5 / 2 -+- 2P 3/ 2 ; 3D 1 -+- 3p o, 51 5-+- 5H,,; (b) of the atoms II, He, Li, Be, B, and C? 27. Draw the diagram of allowed transition between the %P 3/2 and 28 1 / 2 terms in a weak magnetic fIeld.

8 /lB in a weak magnetic field. The gas is under normal pressure and temperature. 47. A paramagnetic gas consisting of atoms in the 28 1 / 2 state is in a magnetic field B = 25 kG at a temperature of T = 300 K. Calculate the ratio 'Y] = I1NIN, where I1N is the difference in the number of atoms with positive and negative projections of magnetic moments on the field direction, N is the total number of atoms. , ignoring the spatial quantization. 48. Find the magnetic moment of a paramagnetic gas consisting of N atoms in the 28 1 / 2 state at the temperature T in the magnetic field B.

What orders of monochromatic X-ray reflection will disappear on transition from the simple cubic lattice to space- and facecentered ones? The lattice constants are assumed to be equal in all three cases. Consider the reflections from the planes (100), (110), and (111). 18. 23. Calculate the Madelung constant for a unidimensional crystal, that is, a chain of ions with alternating positive and negative charges. In calculations use the expansion of the function In (1 x) into a series. 24. 3), find: (a) the expression for the binding energy of ionic crystal at equilibrium; (b) the refractive index n of NaCI and CsCI crystals (see Fig.

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