Aparticle of mass iii rests upon an impenetrable horizontal floor located at z = 0 in a uniform gravitational field. (a) what is the one-dimensional hamiltonian (energy operator) for this system? sketch the potential energy. (b) sketch the wave function for the ground state of the hamiltonian as a fun cti on of z . indicate on your sketch the approximate location of (z), the average height of the particle above the floor. (e) assume you can approximate (z) ~ 1),0 , where i), z is the uncertainty in the position of the part icle. use the heisenberg uncertainty principle

Uranium has two naturally occurring isotopes. 238u has a natural abundance of 99.3% and 235u has an abundance of 0.7%. it is the rarer 235u that is needed for nuclear reactors. the isotopes are separated by forming uranium hexafluoride uf6, which is a gas, then allowing it to diffuse through a series of porous membranes. 235uf6 has a slightly larger rms speed than 238uf6 and diffuses slightly faster. many repetitions of this procedure gradually separate the two isotopes. what is the ratio of the rms speed of 235uf6 to that of 238uf6? express your answer to five significant figures.