Calculating the energy of a hydrogen atom

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SUMMARY

The discussion focuses on calculating the number of different photon energies emitted by hydrogen atoms transitioning from the n=5 state to the ground state (n=1). The relevant equations include the Rydberg formula for hydrogen, given by 1/lambda = R*(1/m^2 - 1/n^2), where R is the Rydberg constant (1.097 x 10^7 m^-1). The user speculates that the number of transitions can be determined using combinations, specifically 5 choose 2, to account for the various possible transitions between energy levels.

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  • Understanding of quantum mechanics and atomic energy levels
  • Familiarity with the Rydberg formula for hydrogen
  • Knowledge of combinatorial mathematics, specifically combinations
  • Basic principles of photon emission and energy transitions
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  • Study the Rydberg formula in detail and its application to hydrogen atom transitions
  • Learn about quantum state transitions and their implications for photon emission
  • Explore combinatorial mathematics, focusing on calculating combinations
  • Investigate the concept of energy levels in hydrogen and other atoms
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Students studying quantum mechanics, physicists interested in atomic transitions, and educators teaching atomic structure and photon emission principles.

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Homework Statement



A sample of hydrogen atoms are all in the n=5 state. If all the atoms return to the ground state, how many different photon energies will be emitted , assuming all possible transitions occur?

Homework Equations


possible equation: E= hc/lambda =(E(initial) -E(final)) .
1/lambda = R*(1/m^2-(1/n^2))

The Attempt at a Solution



Not sure where to begin on this problem, but I suspect I should find the energy of the hydrogen atom between the transitons of the two state. I know n=1 for the ground state.

1/lambda=1.097*10^7*(1/1^2-(1/5^2))

Not sure how to find the Number of photon energies :(
 
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why hasn't anyone answer my question
 
Wouldn't you just have 1 possible transition for every 2 states... so using combinations wouldn't the answer be 5 choose 2?
 

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