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Consider an electron in a one-dimensional box of length 2.000 Å with the left end of the box at x = 0.
(a) Suppose we have one million of these systems, each in the n = 1 state, and we measure the x coordinate of the electron in each system. About how many times will the electron be found between 0.600 Å and 0.601 Å? Consider the interval to be infinitesimal.
(b) Suppose we have a large number of these systems, each in the n = 1 state, and we measure the x coordinate of the electron in each system and find the electron between 0.700 Å and 0.701 Å in 126 of the measurements. In about how many measurements will the electron be found between 1.000 Å and 1.001 Å?
An uncontracted, horizontal weir (sharp-crested) is 4.5 m long and 3.1 in high. Determine the discharge if the upstream water depth is 4.4 m. Determine the discharge for the same upstream depth if a contracted weir (both ends) with a 2.4-m crest length and the same height is being proposed as a replacement for the original weir. Assume the same discharge coefficient.
