Diatomic chain. Consider the normal modes of a linear chain in which the force constants between the nearest-neighbor atoms are C and 10C. Let the masses be equal and let the nearest-neighbor separation be a/2. Find w(K) at K = 0 and K = π/a. Sketch in the dispersion relation by eye. The problem simulates a crystal of diatomic molecules such as H₂.

Charge is distributed over a triangular region in the xy-plane bounded by the y-axis and the lines y = 5 – x and y = 1+ x. The charge density at a point (x, y) is given by o(x, y) = x + y, measured in coulombs per square meter (C/m 2). Find the total charge. Select one: О а. 4 С b. 68 C 3 44 C 3 O c. O d. 20 37 C 3 е.

A particle is in a box with infinitely rigid walls. The walls are at x = -L/2 and x = +L/2.Show that cn = A cos knx is a possible solution.

The greenhouse-gas carbon dioxide molecule CO2 strongly absorbs infrared radiation when its vibrational normal modes are excited by light at the normal-mode frequencies. CO₂ is a linear triatomic molecule, as shown in (Figure 1), with oxygen atoms of mass mo bonded to a central carbon atom of mass mc. You know from chemistry that the atomic masses of carbon and oxygen are, respectively, 12 and 16. Assume that the bond is an ideal spring with spring constant k There are two normal modes of this system for which oscillations take place along the axis. (You can ignore additional bending modes.) In this problem, you will find the normal modes and then use experimental data to determine the bond spring constant. Figure O 1 mo T X₁ k C 2 mc 1X₂ k 1 of 1 > O 3 mo 1 X3 Part A Let ₁, 2, and 3 be the atoms' positions measured from their equilibrium positions. First, use Hooke's law to write the net force on each atom. Pay close attention to signs! For each oxygen, the net force equals mod²x/dt².…