What is the formula for the width of the potential box?

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SUMMARY

The discussion centers on calculating the width of a potential box (L) for an excited electron transitioning from quantum number 4 to the ground state, emitting a photon that excites a hydrogen atom's electron to quantum number 3. The relevant equations include the energy levels of hydrogen, given by E = -13.6/n² eV, and the frequency formula, frequency = 3.29 x 1015 x Z²(1/nfinal - 1/ninitial), which relates to photon emission. The user seeks clarity on when to apply these equations and the specific formula for calculating the width of the potential box.

PREREQUISITES
  • Understanding of quantum mechanics, specifically energy levels of electrons in hydrogen atoms.
  • Familiarity with the concept of potential boxes in quantum physics.
  • Knowledge of Planck's equation, E = hf, for photon energy calculations.
  • Basic algebra for manipulating equations and solving for variables.
NEXT STEPS
  • Research the derivation of the width of a potential box using the formula L = nλ/2, where λ is the wavelength of the emitted photon.
  • Study the relationship between energy transitions in hydrogen and photon emission using the Rydberg formula.
  • Explore the implications of quantum numbers on electron energy states and transitions.
  • Learn about the uncertainty principle and its relevance to particle confinement in potential boxes.
USEFUL FOR

Students and educators in quantum mechanics, physicists interested in atomic transitions, and anyone studying the behavior of electrons in potential wells.

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Homework Statement


An excited electron (quantum number =4) in a 1D potential box de-excites to the ground state and emit a photon. This photon subsequently becomes absorbed by an electron in a hydrogen atom. The electron in the hydrogen atom becomes excited to an excited state with quantum number =3. The process is illustrated in the following diagram. Determine the width of the potential box L.


Homework Equations


n(subscript n)=-13.6/n^2 eV

or frequency= 3.29x10^15 x Z^2(1/nfinal-1/ninitial) then use E=hf. I actually don't really understand when to use which equation. Can someone kindly explain to me?

Also, what is the formula to calculate the width of the particle in box box?
Thank you very much!

The Attempt at a Solution

 
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Think about the energies of the original electron, the photon it emits, and the hydrogen atom's electron.
 

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