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The expectation value, in quantum mechanics, is the probabilistic value of the result. Using the formula for expectation value we can find the expectation value.
Note:- as neither expression for the wave function not the limits are given I am leaving the expression for expectation value of r only
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- (100) An clectron is confined to a region of space that is L distance long (this is the "particle in a box" problem discussed in class). Draw a diagram of the allowed wave functions for the electron's first four energy levels. Also draw the square of the wave functions on your diagram. What are the wavelengths of each of these wave functions? n = 4 E4 n = 3 Ез E2 E, For the fourth energy level, what is the probability of finding the clectron in the far left quarter of the box?. Suppose a quanton's wavefunction at a given time is y(x) = A[1 + (x/a)2]-¹, where A is an unspecified constant and a = 4.0 nm. According to the table integrals dx √ [1 + (x/a)²]² = 1 + (x/a)²+2tan ¹ (2) If we were to perform an experiment to locate the quanton at this time, what would the probability of a result between x = 0 and x = 8.0 nm?3. Suppose an electron in a hydrogen atom is in a 2p state, and the radial wavefunction e 2ao, where a, is the Bohr radius. 1 is (2ао)3/2 VЗа. (а) What possible angles might the angular momentum vector L make with the Z-axis? (b) What is the most probable radius (in terms of a.) at which the electron is found? (c) What is the expectation value of r in this state? Note: S xe-"dx 120. (d) What is the probability of finding such an electron between a, and ∞? Note: ° x*e-"dx = 23.91.