Explanation Write the expression to obtain the energy level for different transition states. Δ E = h c λ (I) Here, Δ E is the energy level for different transition states, h is the Planck’s constant, c is the speed of the light and λ is the wavelength. The expression of the energy level for a particle in a rigid well is given as, Δ E = h 2 8 m l 2 ( ( n ' ) 2 − n 2 ) (II) Here, Δ E is the energy level for different transition level, h is the Planck’s constant, m is the mass of the electron, l is the width of the well n is the initial transition state and n ' is the final transition state. Compare equation (I) and (II). h c λ = h 2 8 m l 2 ( n ' 2 − n 2 ) c λ = h 8 m l 2 ( n ' 2 − n 2 ) l 2 = h λ 8 m c ( n ' 2 − n 2 ) l = h λ 8 m c ( ( n ' ) 2 − n 2 ) Conclusion: The photon has the longest wavelength in case of the lowest energy. Thus the lowest energy transition take place when n = 1 and n ' = 2 . Substitute 6.63 × 10 − 34 J ⋅ s for h , 9

Physics for Scientists and Engineers (Chaps 1-38)

4th Edition

ISBN: 9780132275590

Author: Douglas C. Giancoli

Publisher: Addison-Wesley

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Chapter 38, Problem 26P

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The width of the well for the given conditions.

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Physics for Scientists and Engineers (Chaps 1-38)

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The width of the well for the given conditions.

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Chapter 38 Solutions