Let it'"(r) denote a simultaneous eigenfunction of the angular momentum operators l2 and lz. the respective eigenvalues are l(+1)ћ2 and тћ, with l a nonnegative integer and m =-1,-i + 1, . . , i (a) an atom is prepared with wavefunction consider separately measurements of l and lz. (i) what are the possible results of the measurement in each case? (ii) with what probability does each result occur? (b) a beam of atoms prepared in state v(r) enters a region of uniform magnetic field ib oriented in the r direction. the potential energy of interaction between each atonm and the magnetic field yields hamiltonian where is a constant. what is the state of an atom after it has spent a time t in the magnetic field? (c) the beam leaves the region of uniform field after a time t and the z-component of angular momentum is measured. for what proportion of the atoms is the result obtained?

An internally reversible refrigerator has a modified coefficient of performance accounting for realistic heat transfer processes of where qin is the refrigerator cooling rate, qout is the heat rejection rate, and is the power input. show that copm can be expressed in terms of the reservoir temperatures tc and th, the cold and hot thermal resistances rt,c and rt,h, and qin, as where rtot rt,c rt,h. also, show that the power input may be expressed as 1.39 a household refrigerator operates with cold- and hot-temperature reservoirs of tc 5 c and th 25 c, respectively. when new, the cold and hot side resistances are rc,n 0.05 k/w and rh,n 0.04 k/w, respectively. over time, dust accumulates on the refrigerator’s condenser coil, which is located behind the refrigerator, increasing the hot side resistance to rh,d 0.1 k/w. it is desired to have a refrigerator cooling rate of qin 750 w. using the results of problem 1.38, determine the modified coefficient of performance and the required power input w under (a) clean and (b) dusty coil conditions. internally reversible refrigerator qout qin w high-temperature reservoir low-temperature reservoir th th,i tc,i tc high-temperature side resistance low-temperature side resistance w qin th tc qinrtot tc qinrtot copm tc qinrtot th tc

If y gets smaller as x gets bigger and y have an relationship?

Two steel balls, each of mass m, are welded to a light rod of length l and negligible mass and are initially at rest on a smooth horizontal surface. a horizontal force of magnitude f is suddenly applied to the rod as shown. determine (a) the instantaneous acceleration a of the mass center g and (b) the corresponding rate at which the angular velocity of the assembly about g is changing with time.