Photon Emission and Energy Levels in a Hydrogen Atom

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SUMMARY

The discussion focuses on calculating the energy absorbed by a hydrogen atom when it transitions from the n=1 state to the n=4 state, utilizing the formula E(n)=(-A)/(n^2) with A=13.6 eV. The energy difference between these two states is critical, as it cannot exceed 13.6 eV. Participants emphasize the importance of correctly calculating the energy difference to determine the emitted photon energies as the atom returns to the n=1 state.

PREREQUISITES
  • Understanding of quantum mechanics and energy levels in atoms
  • Familiarity with the hydrogen atom model
  • Knowledge of energy calculations using E(n)=(-A)/(n^2)
  • Basic skills in interpreting energy-level diagrams
NEXT STEPS
  • Research the calculation of energy differences in quantum states of hydrogen
  • Learn about photon emission and absorption processes in quantum mechanics
  • Explore energy-level diagrams and their significance in atomic transitions
  • Study the implications of the Rydberg formula for hydrogen transitions
USEFUL FOR

Students of physics, particularly those studying quantum mechanics, educators teaching atomic theory, and anyone interested in the behavior of hydrogen atoms and photon interactions.

Owen-
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Homework Statement



A hydrogen atom is excited from the state with n=1 to that with n=4. Calculate the energy (in eV) that must be absorbed by the atom. Calculate and display on an energy-level diagram the different photon energied (in eV) that may be emitted in order for the atom to reach the n=1 state


Homework Equations



E(n)=(-A)/(n^2)

A=13.6


The Attempt at a Solution



See attached image
 

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Basically I got a couple of answers and none of them add up, and I am wondering where I've gone wrong...

thanks in advance,
Owen
 
This belongs in intro physics...

The only thing wrong with your solution is your E4 - E1 calculation. Think about what it means to go from n=1 to n=4 and the energy DIFFERENCE between these 2 levels (Hint, your answer by definition cannot be greater than 13.6eV)
 

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