Why Is the Calculated Wavelength Incorrect in This Hydrogen Atom Problem?

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SUMMARY

The discussion centers on the calculation of the wavelength of a photon emitted during the transition of an electron from the first excited state to the ground state in a hydrogen atom. The correct approach involves using the energy formula E = -13.6 (z/n)^2 to find the energy difference between the two states, followed by E = hc/λ to determine the wavelength. The correct wavelength for this transition is 6.68 Ångström. Misunderstanding the question led to confusion between the energy of the excited state and the wavelength of the emitted photon.

PREREQUISITES
  • Understanding of quantum mechanics principles, specifically energy levels in hydrogen atoms.
  • Familiarity with the formula E = -13.6 (z/n)^2 for calculating energy levels.
  • Knowledge of the relationship between energy and wavelength using E = hc/λ.
  • Awareness of the concept of photon emission during electron transitions.
NEXT STEPS
  • Study the derivation and application of the Rydberg formula for hydrogen spectral lines.
  • Learn about the deBroglie wavelength and its significance in quantum mechanics.
  • Explore the concept of energy level transitions in other elements beyond hydrogen.
  • Investigate the implications of quantum mechanics on atomic structure and electron behavior.
USEFUL FOR

Students studying quantum mechanics, physics educators, and anyone interested in atomic theory and photon emission processes.

Suyash Singh

Homework Statement


Calculate energy of electron in first excited state of hydrogen atom.

Homework Equations


n=2
when i use E=-13.6 (z/n)^2
and then use E=hc/lamda(wavelength)
then wavelength is coming wrong

The Attempt at a Solution


the correct answer is 6.68 armstrong.
 
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Ångström (not armstrong) is a unit of length, not a unit of energy. It is likely that you are not being asked what you have stated that you are being asked about here. The question is likely what the wavelength of the photon emitted when the electron in the first excited state of hydrogen transits to the ground state. This is not the same thing as the energy in the first excited state.
 
Suyash Singh said:
when i use E=-13.6 (z/n)^2
and then use E=hc/lamda(wavelength)
then wavelength is coming wrong
Are you trying to find the deBroglie wavelength of the electron when it is in the first excited state? If so, the formula E = hc/λ is not the correct formula.
 

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