A photon with wavelength is absorbed by anelectron confined to a box. As a resul

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.

Explanation / Answer

hc/ = E = energy of photon = change in energy of theelectron. e = 2L/n = wavelength of the electron in the box. p = h/e = nh/2L = DeBroglie wavelength of the electron. E = p2/2m =n2h2/8mL2. So, E =[h2/8mL2]*(nfinal2 -ninitial2) (a) For a transition from n=1 to n=7, (hc/) = (6h2/m)/L2. Thus, L = [6h/mc] (b) For a transition from n=7 to n=2, the emitted photon has an energy : -E = (hc/') = -[h2/8mL2]*(4 - 49)= 45[h2/8mL2] So, ' = [8mL2c/45h]

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