Excited hydrogen atom and wavelength

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SUMMARY

A hydrogen atom in its ground state can be excited to the n=5 level and subsequently transition to the n=2 level, emitting photons in the process. The energy difference between these levels is calculated as ΔE = E_final - E_initial = -3.40 eV - (-0.54 eV) = -2.86 eV. Using the equation λ = hc/E, the wavelength of the emitted photon can be determined. This transition emits light, some of which falls within the visible spectrum.

PREREQUISITES
  • Understanding of quantum mechanics and energy levels in hydrogen atoms
  • Familiarity with the equation E = (hc)/λ for photon energy and wavelength
  • Knowledge of electron transitions and conservation of energy
  • Basic understanding of the electromagnetic spectrum, particularly the visible region
NEXT STEPS
  • Calculate the wavelengths of emitted photons for transitions in hydrogen using E = (hc)/λ
  • Explore the visible spectrum and identify wavelengths corresponding to visible light
  • Study the concept of energy level diagrams for hydrogen and other elements
  • Investigate the implications of electron transitions in spectroscopy
USEFUL FOR

Students studying quantum mechanics, physics educators, and anyone interested in atomic transitions and spectroscopy.

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i have been working on this question for quite a while. no help on google, or my textbook at all.

A hydrogen atom in its ground state is excited to the n=5 level. It then makes a transition directly to the n=2 level before returning to the ground state.

A) What are the wavelengths of the emitted phontons?

B)Would any of the emmitted light be in the visible region?

I have searched through my textbook and there is no examples to work off of nor much information on this topic really. so if anyone could help that would be greatly appreciated.
 
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This is my guess at how to do this question (I'm referring to my high school notes for this...)

Basically, you can use the good old E=(hc)/lambda.
Wavelength (lambda) will equal hc/E.

Now, if you look at this diagram:
[PLAIN]http://castlelearning.com/review/reference/phys6.gif

you can see that when n=5, E of electron is -0.54eV. At n=2, E=-3.40eV.
When the electron moves from n=5 to n=2, it loses Ef-Ei=-3.40-(-0.54) eV=-2.86eV
That means that the photon is emitted with that same energy (conservation of energy). So, Ep=2.86eV.
From which, you can find the wavelength using equation I stated above.

I hope this helps :)
 
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