5. Consider an electron trapped by a positively charged point defect in a one-dimensional world. The following wavefunction with α = 20/nm describes the distance x of the electron from the point defect located at x=0. Note that in 1, 2, and 3 dimensions, r = |x|, (x²+y²)^(1/2), and (x²+y²+z²)^(1/2), respectively.\[ \psi(r) = Ne^{-\alpha |x|} \]1. Evaluate the normalization constant N.2. Graph the probability density for this electron.3. Calculate the expectation value for x and |x|.4. If the electron were in a two or three-dimensional world, such as on the surface of a crystal or in a free atom, would the average distance of the electron from the origin be less, the same, or larger than the value you found for one dimension?5. Determine whether the expectation value for r depends upon the dimensionality of the world (1, 2, or 3) in which the atom lives.

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Answered: 5. Consider an electron trapped by a…

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