A photon with wavelength is absorbed by anelectron confined to a box. As a resul
ID: 1679753 • Letter: A
Question
A photon with wavelength is absorbed by anelectron confined to a box. As a result, the electron moves fromstate n = 1 to n = 7. (a) Find the length of the box. Express yourresult using h, m, c, and lambda to represent Planck's constant,the electron's mass, the speed of light, and ,respectively.(b) What is the wavelength of the photon emitted in the transitionof that electron from the state n = 7 to the state n = 2? Express your resultusing the same variables specified in the previous part.
(a) Find the length of the box. Express yourresult using h, m, c, and lambda to represent Planck's constant,the electron's mass, the speed of light, and ,respectively.
(b) What is the wavelength of the photon emitted in the transitionof that electron from the state n = 7 to the state n = 2? Express your resultusing the same variables specified in the previous part.
(b) What is the wavelength of the photon emitted in the transitionof that electron from the state n = 7 to the state n = 2? Express your resultusing the same variables specified in the previous part.
Explanation / Answer
wave length of photon 1 / = R ( 1 / 1 - 1 / 49) = (1.09*107) = 9.3*10-6 m energy of the photon E = h c / electron gains the energy for the jumpfrom energy level E 1 to E7 by absorbing light is E = (h 2 / 8 mL 2 ) ( 7 2 - 1 2 ) h c / = (h 2 / 8 m L 2 ) 48 length of the box L = ( 48 h / 8m c ) = ( 48*6.635*10-34 *9.3*10-6 / 8* 9.1*10-31*3*108 ) = 1.16*10-8 m electron gains the energy for the jumpfrom energy level E 7 to E2 by absorbing light is energy ofphoton E = (h2 / 8 m L 2 ) ( 7 2 -2 2 ) = [ (6.635*10-34 ) 2 / 8 ( 9.1*10-31 )(1.16*10-8 ) ]45 = 2*10-20 J wave length ofphoton = h c / E = ( 6.635*10-34 )(3*108 ) /(2*10-20 ) = 9.952*10-6 m
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