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.)

Which is the best predictor of the radioactive nature of an isotope? o the proton-to-electron ratio the neutron-to-proton ratio o the neutron-to-electron ratio the electron-to-proton ratio

As you are trying to move a heavy box of mass m, you realize that it is too heavy for you to lift by yourself. there is no one around to , so you attach an ideal pulley to the box and a massless rope to the ceiling, which you wrap around the pulley. you pull up on the rope to lift the box. use g for the magnitude of the acceleration due to gravity and neglect friction forces. once you have pulled hard enough to start the box moving upward, what is the magnitude f of the upward force you must apply to the rope to start raising the box with constant velocity? express the magnitude of the force in terms of m, the mass of the box.

Where is the potential energy throughout the loading, cocking, and releasing of the trebuchet?