Length of a one-dimensional box with an electron inside

HuntMBryan

Another student was asking me about how to calculate L in a one-dimensional box, given that an electron with a wavelength of 418nm moves from energy-level n=2 to energy-level n=4.


Using, ΔE = E_f - E_i, I can say that ΔE = E₄ - E₂ = ((4² - 2²) * h² ) / (8mL²)

Rearranging for L is simple, but I was unsure on how to get ΔE. I used de Broglie to get speed and put that speed into KE = (1/2)mu² and the teacher told me not to use that.

One of the lab teachers was telling me to use c = λv to get v and then use E = hv to calculate the energy that the electron absorbs to move from n₂ to n₄.

My question is why we are using E = hv. Why is light being associated with the electron?

SpectraCat

The question as stated in your original post is mis-phrased. The wavelength referenced in the problem is not the deBroglie wavelength of the electron as implied, but rather the wavelength of light absorbed by the electron in making a transition between the n=2 and n=4 levels. That is why you use the Planck equation to calculate the photon energy from the wavelength of light used.

HuntMBryan

Yeah, I was wondering about that. I'll go see if I can pull up the original problem. The wording was really really bad.