An alpha particle collides with an oxygen nucleus, initially at rest. the alpha particle is scattered at an angle of 42.0° above its initial direction of motion, and the oxygen nucleus recoils at an angle of 49.0° below this initial direction. the final speed of the oxygen nucleus is 1.60×10^5 m/s. (the mass of an alpha particle is 4.0 u, and the mass of an oxygen nucleus is 16 u.) what is the final speed of the alpha particle?

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.