Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.
••“The average distance D between the atoms or molecules in a gas is of order D ≈ 3 nm at atmospheric pressure and room temperature. This distance is much larger than typical atomic sizes, and it is, therefore, reasonable to treat an atom as an isolated system, as we did in our discussion of hydrogen. However, the Bohr theory predicts that the radius of the nth orbit is n2aB. Thus for sufficiently large n, the atoms would be larger than the spaces between them and our simple theory would surely not apply. Therefore, one would not expect to observe energy levels for which the atomic diameter 2n2aB is of order D or more, (a) At normal densities (with D ≈ 3 nm) what is the largest n that you would expect to observe? (b) If one reduced the pressure to 1/1000 of atmospheric, what would be the largest n? [Remember that the spacing D is proportional to (pressure)−1/3 for constant temperature.] (c) Modern experiments have found hydrogen atoms in levels with n ≈ 100. What must be the pressure in these experiments?
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.