How is a quarter wavelength in the pipe
going to change the math?

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.

Light from a sodium lamp passes through a diffraction grating that has 1000 slits per millimeter. the interference pattern is viewed on a screen 1.000 m behind the grating. the first (m = 1) two bright yellow fringes that are visible are 0.7288 m and 0.7300 m from the central maximum. what are the wavelengths of these two fringes?

Scientific models are based on current knowledge, which can limit their effectiveness when new discoveries are made.