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suppose a hypothetical object has just four quantum states, with the following energies:

-0.3 ev (third excited state)
-1.0 ev (second excited state)
-2.4 ev (first excited state)
-4.7 ev (ground state)

suppose that the beam of electrons is shut off so that all of the objects are in the ground state almost all the time. if electromagnetic radiation with a wide range of energies is passed through the material, what will be the three energies of photons corresponding to missing ("dark") lines in the spectrum? remember that there is hardly any absorption from excited states, because emission from an excited state happens very quickly, so there is never a significant number of objects in an excited state. assume that the detector is sensitive to a wide range of photon energies, not just energies in the visible region. list the dark-line energies in order from largest to smallest.
ev (largest)
ev
ev (smallest)

Acatapult is tested by roman legionnaires. they tabulate the results in a papyrus and 2000 years later the archaeological team reads (distances translated into modern units): range = 0.4 km; angle of launch = π/5 rad; landing height = launch height. what is the initial velocity of launch of the boulders if air resistance is negligible?

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

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