In-class problems 6 Solutions

# In-class problems 6 Solutions - ≤ x ≤ L ψ 2 x = r 2 L...

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Name Student ID Section In-Class Problem, Week 9 3 June 2008 Show ALL your work, Total Points Possible = 8 1. A photon with wavelength λ is absorbed by an electron conﬁned to a box. As a result, the electron moves from state n = 1 to state n = 4. (a) Find the length of the box. Express your result using ¯ h,m,c,λ . (+ 2 pt) Δ E = π 2 ¯ h 2 2 mL 2 (4 2 - 1 2 ) = 2 π ¯ hc λ L = q 15 π ¯ 4 mc (b) What is the wavelength of the photon emitted in the transition of that electron n = 4 to the state n = 2? Express your results using the same variables speciﬁed in part (a). (+ 2 pt) 12 π ¯ h 2 mL 2 = 2 c λ 0 use L 2 from (a) λ 0 = 15 12 λ 2. A particle in an inﬁnitely deep square well has a wave function given by the equation below where 0
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Unformatted text preview: ≤ x ≤ L. ψ 2 ( x ) = r 2 L sin ( 2 πx L ) (1) The expectation value of x is L 2 . Sketch the square of the wave function and show where the particle is most likely to be. Why do these points diﬀer from the expectation value of x? (+ 4 pt) The most likely positions are around x = L 4 and x = 3 L 4 . It is clear from the plot of the probability density that it maximized around these positions. However, the symmetry forces the expectation value of position to L 2 . Some possibly useful equations: E n = n 2 h 2 8 mL 2 , h = 2 π ¯ h E photon = hf = hc λ < x > = R L ψ * xψ dx 1...
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