Calculating the width of the box for a particle in a box

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SUMMARY

The discussion focuses on calculating the width of a quantum box for an electron transitioning between energy states, specifically from n=2 to n=1, using a ruby laser with a wavelength of 694.3 nm. The wavenumber K is calculated using the formula K = 2π/λ, resulting in a value of 9049669. The participant expresses confusion regarding the relationship between K and k, where k represents the wavenumbers of the electron wavefunctions defined by k = nπ/L. To find the box width L, the energy difference between the electron states must be equated to the energy of the emitted photon.

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  • Understanding of quantum mechanics principles, specifically particle in a box model.
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  • Ability to manipulate and solve equations involving wavefunctions.
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Homework Statement



A ruby laser emits light of wavelength 694.3 nm. If this light is due to the transition from n=2 to n=1 state of the electron in a box, what is the width of the box?

Homework Equations



K=2pi/Lambda
kL=npi

The Attempt at a Solution


Thinkin about the problem, i have calculated K as shown in my formula to be 9049669 but when i use this k to find L then i end up with 694.3 again. I don't know if this is the answer or if this is a really big mistake?
 
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The K and k in those equations are not the same. [tex]K = 2\pi/\lambda[/tex] is the wavenumber of the emitted photon. [tex]k = n\pi/L[/tex] are the wavenumbers of the electron wavefunctions. You need to compute the difference in electron energy levels and equate that to the energy of the photon.
 

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