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By I. E Irodov

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Interaction energy as a function of the distance bet ween the nuclei of a diatomic molecule is shown in Fig. 23, where D is the dissociation energy. • Mean energy of a quantum harmonic oscillator (E)= n00 2 + en6J /noo kT -1 . 3) • Fig. 24 illustrates the diagram describing the emergence of red (a) and violet (b) satellites in the Raman scattering of light. 1. Using the tables of the Appendix, find for H 2 and NO molecules: (a) the energy required for their promotion to the first rotational level (J = 1); (b) the angular rotation velocity in the state with J = 1.

Find the ratio of HBr molecules being in purely vibrational states (without rotation) with quantum numbers v = 2 and v = 1 aliT = 910 K. At what temperature will that ratio be equal to 1 : 10? 17. 5), determine the ratio of the number of hydrogen molecules in the states with quantum numbers v' = 1, J' = 0 to those with v = 0, J = 5 at T = 1500 K. 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).

Using the Fermi distribution, find at 0 K: (a) the mean kinetic energy of free electrons in a metal, if their highest kinetic energy T max is known; (b) the total kinetic energy of free electrons in 1 cm 3 of gold, assuming one free electron to correspond to each atom. 4. What fraction of free electrons in a metal at 0 K has a kinetic energy exceeding half the maximum energy? 5. Calculate the temperature of an ideal gas consisting of particles whose mean kinetic energy is equal to that of free electrons in copper at 0 K.

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


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