Explanation Given Information: Wave length λ = 450 nm Formula Used: The energy of a λ photon can be calculated using the following relation, E = h c λ Calculation: Transition is in between ground state having quantum number ( n x , n y , n z ) = ( 1 , 1 , 1 ) and one of the three states of next highest energy having quantum number ( n x , n y , n z ) = ( 2 , 1 , 1 ) , ( 1 , 2 , 1 ) , or ( 1 , 1 , 2 ) The energy of a λ photon can be calculated using the following relation. E = h c λ Substitute 6 .62607×10 -34 J .s for h, 2 .9979×10 8 m/s for c, and 450 nm for λ in the equation E = h c λ . E = h c λ = ( 6 .62607×10 -34 J .s ) ( 2 .9979×10 8 m/s ) 450×10 -9 m = 4.41 43×10 -19 J This must equal the difference of the first excited state energy and ground state energy, which is given by, E 112 − E 11 1 = ( 1 2 + 1 2 + 2 2 ) π 2 ℏ 2 2 m L 2 − ( 1 2 + 1 2 + 1 2 ) π 2 ℏ 2 2 m L 2 = 3 π 2 ℏ 2 2 m L 2 Set the transition energy equal to the energy of the photon E 112 − E 11 1 = h λ c 3 π 2 ℏ 2 2 m L 2 = 4

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ISBN: 9780805303087

Author: Randy Harris

Publisher: Addison Wesley

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Schrödinger equation

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Chapter 7, Problem 21E

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Width of the well

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