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Consider an electron confined to a box of length L = 436 pm. (a) A transition between energy levels can be induced by absorption of light whose photon energy matches the energy difference between the levels. Find the energy difference between the levels corresponding to n = 4 and n = 5 of this same box, and compute the wavelength of light (in m) that would cause a transition between them. What portion of the electromagnetic spectrum is this light? (b) For another box, suppose that this same transition (n=45) was observed at a wavelength of 232 nm. How long is this box in pm?

Consider an electron confined to a box of length L = 436 pm. (a) A transition between energy levels can be induced by absorption of light whose photon energy matches the energy difference between the levels. Find the energy difference between the levels corresponding to n = 4 and n = 5 of this same box, and compute the wavelength of light (in m) that would cause a transition between them. What portion of the electromagnetic spectrum is this light? (b) For another box, suppose that this same transition (n=45) was observed at a wavelength of 232 nm. How long is this box in pm?

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A) Report your answer as a decimal number with three signficant figures.

B)Give your answer as a decimal number with three significant figures.

C) How does the classical kinetic energy of the free electron compare in magnitude with the result you obtained in the previous part?

 

Consider an electron confined to a box of length L = 436 pm. (a) A transition between energy levels can be induced by absorption of light whose photon energy matches the energy difference between the levels. Find the energy difference between the levels corresponding to n = 4 and n = 5 of this same box, and compute the wavelength of light (in m) that would cause a transition between them. What portion of the electromagnetic spectrum is this light? (b) For another box, suppose that this same transition (n = 4 →5) was observed at a wavelength of 232 nm. How long is this box in pm?
Transcribed Image Text:Consider an electron confined to a box of length L = 436 pm. (a) A transition between energy levels can be induced by absorption of light whose photon energy matches the energy difference between the levels. Find the energy difference between the levels corresponding to n = 4 and n = 5 of this same box, and compute the wavelength of light (in m) that would cause a transition between them. What portion of the electromagnetic spectrum is this light? (b) For another box, suppose that this same transition (n = 4 →5) was observed at a wavelength of 232 nm. How long is this box in pm?
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