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

By I. E Irodov

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35. J = 0, +2) are descnbed by the formula (t) = (t) 0 + 2B (2k 1); k = 1, 2, 3, . , + where (t)o is the fixed line frequency and B rotational constant. (a) Derive this formula. 8 cm -1. 36. 2 A for N molecules. vf these molecules. 5) 6 where R is the universal gas constant, 8 is the Debye characteristic tPrtl\wraLure, Wmax is the maximum vibration frequency calculated from thp condition that the total number of vibrations is equal to the numbpr of vibrational degrpes of freedom in a crystal. Molar vibrational heat capacity of a crystal at T 8: «:: f' Period of identity is a distance between the neirrhbourin<' identical atoms along a certain direction in a lattice.

32. At what value of magnetic field will the interval between (J' components of the Li resonance line exceed ten-fold the value of natural splitting of that line? 80 A.. 33. Show that the frequency of transition between the neighbouring sublrwels of the Zeeman term splitting coincides with the frequency of precession of an angular momentum of atom in a magnetic field. 34. The magnetic resonance occurs when a substance consisting of atoms with inherent magnetic moments is exposed to two magnetic fIelds: the stationary field B and the weak variable field B OJ directed perpendicular to the former one.

Find the quasielastic force constants for H 2 and CO molecules. 7. The potential energy of interaction of atoms in a diatomic molecule can be described approximately by the following formula + where r 0 is the equilibrium nuclear separation, U 0 is the depth of the potential well, a is the intrinsic molecular constant. Calculate the values U o and a for a hydrogen molecule. 8. For a hydrogen molecule calculate: (a) the classical vibration amplitude corresponding to the zero vibrational energy; (b) the root-mean-square value of the vibration coordinate x in the ground state which is described by the wave function '\jJ (x) ex: e- 0h2 / 2 , where a 2 = ftwln; ft is the reduced mass, w is the vibration frequency.

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