What are the bending spring constants for a silicon cantilever with E = 170 GPa, h = 5 µm, w = 2 µm, and L = 100 µm? In real manufacturing, there is likely a dimensional deviation in fabricated device from design values. How much the spring constant change if all dimensions are increased by 5%? How much the spring constant change if all dimensions are decreased by 5%? How much the spring constant change if all dimensions are increased by 200 nm?

Some material consisting of a collection of microscopic objects is kept at a high temperature. a photon detector capable of detecting photon energies from infrared through ultraviolet observes photons emitted with energies of 0.3 ev, 0.5 ev, 0.8 ev, 2.0ev, 2.5ev, and 2.8ev. these are the only photon energies observed. (a) draw and label a possible energy-level diagram for one of the microscopic objects, which has four bound states. on the diagram, indicate the transitions corresponding to the emitted photons. explain briefly. (b) would a spring–mass model be a good model for these microscopic objects? why or why not? (c) the material is now cooled down to a very low temperature, and the photon detector stops detecting photon emissions. next, a beam of light with a continuous range of energies from infrared through ultraviolet shines on the material, and the photon detector observes the beam of light after it passes through the material. what photon energies in this beam of light are observed to be significantly reduced in intensity (“dark absorption lines”)? explain briefly.