Consider the screened coulomb potential of a point charge that arises e. g. inplasma physics: v(r) =kqexp(−r/λ)r, whereλis a constant called screening length. a) (2 pts) determinee(r) associated with potential. b) (2 pts) find the charge distributionrho(r) that produces this potential. (think carefully about what happens at the origin! )c) (2 pts) show by explicit integration overrho(r) that the charge represented by thisdistribution is zero. (if you don’t get zero, think again about what happens atr= 0).d) (2 pts) verify your result from part c) by using gauss’s law.

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.

Agroup of students is studying convection currents. they fill two identical balloons with the same amount of helium. one balloon is placed in a freezer and the other in an area with warm air. after 10 minutes, the balloons are released from a height of 1 meter. which of the following do the students most likely observe? question 2 options: the balloons rise at the same rate. both balloons are the same size. the ballons both rise. the cold ballon is larger than the warm balloon. the cold balloon expands and rises. the warm balloon shrinks and sinks. the warm balloon expands and rises. the cold balloon shrinks and sinks.

Which type of reaction is shown in this energy diagram ?