(Solid state physics) Consider the normal modes of a linear chain in which the force constants between nearest- neighbor atoms are alternately C and 10C. Let the masses be equal, and let the nearest-neighbor separation be a/2. (a) Find the expression for a²(k) for ka<<1. (b) Find the values of @ (k) at k = 0 and k = a. (c) Sketch in the dispersion relation by eye. (d) Discuss the motions for two neighboring atoms for at k = 0 for the corresponding two modes (in the real space). This problem simulates a crystal of diatomic molecules such as H₂. с Vs Us+1 Vs+ 10C C 10C C a

Check Your Understanding If a=3+4i , what is the product a* a?

The Einstein model for a solid assumes the system consists of 3N independent simple harmonic oscillators with frequencies &. Within these assumptions, the heat capacity at constant volume as: Cv=3Nk() (-1)² ² Complete the table for the molar heat capacity at various temperatures under either the Einstein model or high-temperature limit. You might like to use the Wolfram Alpha calculator to do the numerical calculations more easily. Use k-0.695 cm /K. High temperature limit value of molar heat capacity of metal is T 1 K 10 K 50 K -1 Einstein, = 100 cm Einstein, : = 500 cm 1.4021 3.8991 100 K 500 K 2.434E-4 1000 K 6.1499 2434E-4 kJ/mol.

A system containing a single particle in a rigid container at temperature 100 K has a translational partition function of Ztrans = 1.5 × 1012. (a) If the mass of the particle is doubled, what is the new value for ztrans? Report your answer in scientific notation (in Blackboard, 1.23 x 1045 is written 1.23E45).