Explanation Write the expression to obtain the energy level at different transition states. E n = h 2 n 2 8 m l 2 (I) Here, E n is the energy level at different transition states, h is the Planck’s constant, n is the transition level, m is the mass of the electron and l is the distance between the two transition level. Write the expression to obtain the wave function. ψ n = 2 l sin ( n π x l ) (II) Here, ψ n is the wave function for n transition level, l is the distance between the different transition levels. Conclusion: Substitute 6.63 × 10 − 34 J ⋅ s for h , 9.1 × 10 − 31 kg for m , 2.0 nm for λ , and 1 for n in equation (I) to calculate E 1 . E 1 = ( 6.63 × 10 − 34 J ⋅ s ) 2 ( 1 ) 2 8 ( 9.1 × 10 − 31 kg ) ( 2.0 nm ) 2 = ( 6.63 × 10 − 34 J ⋅ s ) 2 8 ( 9.1 × 10 − 31 kg ) ( 2.0 nm × 1 m 10 9 nm ) 2 ( 1.6 × 10 − 19 J 1 eV ) = 4.39569 × 10 − 67 4.6592 × 10 − 66 eV = 0.094 eV Substitute 6.63 × 10 − 34 J ⋅ s for h , 9.1 × 10 − 31 kg for m , 2.0 nm for λ , and 2 for n in equation (I) to calculate E 2 . E 2 = ( 6.63 × 10 − 34 J ⋅ s ) 2 ( 2 ) 2 8 ( 9.1 × 10 − 31 kg ) ( 2.0 nm ) 2 = ( 4 ) ( 6.63 × 10 − 34 J ⋅ s ) 2 8 ( 9.1 × 10 − 31 kg ) ( 2.0 nm ( 1 m 10 9 nm ) ) 2 ( 1.6 × 10 − 19 J 1 eV ) = 4 ( 0.094 eV ) = 0.38 eV Substitute 6.63 × 10 − 34 J ⋅ s for h , 9.1 × 10 − 31 kg for m , 2.0 nm for λ , and 3 for n in equation (I) to calculate E 3 . E 3 = ( 6.63 × 10 − 34 J ⋅ s ) 2 ( 3 ) 2 8 ( 9.1 × 10 − 31 kg ) ( 2.0 nm ) 2 = ( 9 ) ( 6.63 × 10 − 34 J ⋅ s ) 2 8 ( 9.1 × 10 − 31 kg ) ( 2.0 nm ( 1 m 10 9 nm ) ) 2 ( 1

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Chapter 38, Problem 27P

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The lowest four energy levels and wave functions for an electron trapped in an infinitely deep potential well of width 2.0 nm.

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Chapter 38, Problem 26P

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