Consider the following wave functions representing excited states of He: ψa = 1s(1)2s(2)α(1)α(2) ψb = [1s(1)2s(2) + 1s(2)2s(1)][α(1)β(2) − α(2)β(1)] ψc = [1s(1)2s(2) − 1s(2)2s(1)][α(1)β(2) − α(2)β(1)] ψd = [1s(1)2s(2) − 1s(2)2s(1)]α(1)α(2) (a) Determine which of the wave functions are eigenfunctions of the exchange operator, by acting the exchange operator. (b) Determine which are valid wave functions for excited state He, i. e., which have an eigenvalue of -1 and thus are antisymmetric with respect to exchange. (c) Which of the valid wavefunctions has/have the lowest energy

Two flowing streams of argon gas are adiabatically mixed to form a single flow/stream. one stream is 1.5 kg/s at 400 kpa and 200 c while the second stream is 2kg/s at 500 kpa and 100 ? . it is stated that the exit state of the mixed single flow of argon gas is 150 c and 300 kpa. assuming there is no work output or input during the mixing process, does this process violate either the first or the second law or both? explain and state all your assumptions.

What difference(s) did you notice using a pneumatic circuit over hydraulic circuit.explain why the pneumatic piston stumbles when it hits an obstacle.

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.