A1-d nanomechanical oscillator is fabricated on a silicon microchip to have a mechanical resonance frequency of w 2t x 4.3 ghz (a) what are the energies (in ev) of the oscillator ground and first excited states? (b) compare the ground-to-first-excited-state energy difference with the ground-to-first-excited- state energy difference in the hydrogen atom. by how many times is it bigger or smaller? (c) consider the ground state wavefunction for the harmonic oscillator, derived in class. use this to show that the expectation values of the kinetic energy and potential energy operators are equal for this wavefunction. how do these relate to the ground state energy? (d) the oscillator is cooled to its ground state using the methods of laser cooing. given a mass of 31 fg (femtograms), what are the quantum mechanical uncertainties in its position and speed after the cooling if the oscillator remains in the ground state, how low must the temperature be (to avoid excitations to the first excited state)?

In a steady-flow steam power plant system, two adiabatic high-pressure and low-pressure turbines ane used to generate power. superheated steam enters the high-pressure turbine at 8 mpa and 550°c. the steam expands in the high-pressure turbine to a saturated vapor at 3 mpa. in order to increase the powe generation of the power plant, another steam turbine working in a lower pressure ranges is deployed. the outlet vapor from the first turbine is heated up at a boiler to the temperature of 500 c at the constant pressure of first turbine's outlet (3 mpa). then, the vapor enters the second turbine and produces extra work. the exit conditions of the second turbine are 5o kpa and 90 percent quality. if the total power output of the power plant is 25 mw, determine a) the mass flow rate of the water (kg/s). b) heat transfer rate in the boiler (mw). (30 points) 3 mpa 00 c 8 mpa s0 c high pres turbine low pres boiler turbine 50 kpa 3 mpa 09 saturated vapor t heat engine, shown in the figure, operates between high temperature and low temperature of through a heat 4. a carnot tn and tu respectively. this heat engine receives energy from a heat reservoir at t exchanger where the heat transferred is proportional to the temperature difference as ? = k (z,-7, ). it rejects heat at a given low temperature tl. to design the heat engine for maximum work output, find the high temperature, th, as a function of tes and t. (15 points) qe

Calculate the work done by an external agent during an isothermal compression of 1.00 mol of oxygen from a volume of 22.4 l at 10∘c and 1.0 atm pressure to 16.8l

Decreased sensitivity to an unchanging stimulus is known as