Derive the density of stats function for a zero-dimension quantum dot with a parabolic e-k diagram (hint: a 0-d quantum dot has no free motion of its electrons. thus, all the possible quantum states of the electron are packed into the singularity itself. pay attention to symmetries, if any, and also the 2 spins of the electrons.)

An engine undergoes a cycle as shown in the diagram. during a complete cycle the work done by the gas is 28.5×103 j and the energy transferred thermally out is 99.4×103 j. there are 1.5×1024 gas molecules and they have three active degrees of freedom. 6. (6 pts) during which process(es) is energy transferred thermally into the gas? a. 1→2 b. 2→3 c. 4→1 d. 1→2 and 4→1 e. none of the above

Me pl give an example of a collision in real life. use the law of conservation of energy to describe the transfer of momentum. be sure and discuss the momentum before and after the collision occurs. you will need at least 3 sentences to thoroughly answer this question.

Aproton is shot from the negative disk toward the positive disk. what launch speed must the proton have to just barely reach the positive disk?