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

By I. E Irodov

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Assuming that each atom independently orients its spin either parallel or antiparallel to a certain direction and the difference in energies of the atom in these states equals /1E, find: (a) the temperature dependence of C i ; (b) the value of the ratio kTI/1E at which C i reaches a maximum; (c) the ratio C z maxlC lat for the case when C i max corresponds to a temperature T = 81100; 8 is the characteristic temperature. 1) J where f (E) = [1 + e(E-Ej)/hT j _1 is called the Fermi-Dirac is the density of states, E j is the Fermi level.

18. 3). 19. 3), calculate the temperature at which: (a) the mean vibrational energy of a Cl" molecule is twice the zero vibrational energy; (b) the level corresponding to the mean vibrational energy of an O 2 molecule coincides with the fifth rotational level of that molecule (J = 5, v = 0). 20. 3) derive the expression for molar vibrational lfeat capacity of diatomic gas at constant volume. Find the approximate forms of that expressiol'l for low and high temperatures (kT«nw and kT~nw). 21. 3), calculate the molar vibrational heat capacity at constant volume for a gas consisting of Cl 2 molecules at temperatures of 150, 300, and 450 K.

Proceeding ~rom th~se concepts demonstrate that the intervals between the nelghbourmg sublevels deflllecl bv the quantum numbers F, F 1, F 2, . relate as + (F + 1):'(F--r- 2): ... 24. The 2D 3 / 2 term of a 209Bi atom has four component~ of hyperfine splitting with the ratio of the intervals between the n81ghbouring components being equal to 4 : 5 : 6. 25. the P 3/2 ~erm m a atom experience splitting in a weak magnetIC field. Fmd the total number of the Zeeman components. 26. In a strong magnetic field each sublevel of the 2~1/2 ter~ in 42K and s5Rb splits into five and six components respectIvely.

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