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 positive numbers less than 1, the zeros between the decimal point and a non-zero number are blank significant

Aweight lifter raises a 1600 n barbell to a height of 2.0 meters. how much work was done? w = fd a) 30 joules b) 3000 joules c) 320 joules d) 3200 joules

To understand the behavior of the electric field at the surface of a conductor, and its relationship to surface charge on the conductor. a conductor is placed in an external electrostatic field. the external field is uniform before the conductor is placed within it. the conductor is completely isolated from any source of current or charge. part a: which of the following describes the electric field inside this conductor? it is in the same direction as the original external field.it is in the opposite direction from that of the original external field.it has a direction determined entirely by the charge on its surface.it is always zero. part b: the charge density inside the conductor is: 0non-zero; but uniformnon-zero; non-uniforminfinite part c: assume that at some point just outside the surface of the conductor, the electric field has magnitude e and is directed toward the surface of the conductor. what is the charge density η on the surface of the conductor at that point? express your answer in terms of e and ϵ0