Binding energy of an electron in an excited state?

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SUMMARY

The energy required to remove an electron from a hydrogen atom in an excited state with n = 8 is calculated using the formula E = - (1 / 4pi*epsilon_0)(me^4/2(h-bar)^2)(1/n^2). By substituting n = 8 into the equation, the binding energy is determined to be approximately 0.2124 eV. This calculation follows the established principle that the binding energy decreases as the principal quantum number n increases, demonstrating a clear symmetry in the energy levels of the hydrogen atom.

PREREQUISITES
  • Understanding of quantum mechanics and atomic structure
  • Familiarity with the hydrogen atom model
  • Knowledge of the formula for binding energy in quantum states
  • Basic proficiency in manipulating mathematical equations
NEXT STEPS
  • Study the derivation of the binding energy formula for hydrogen atoms
  • Explore the concept of quantum numbers and their significance in atomic physics
  • Learn about energy level transitions in hydrogen and other atoms
  • Investigate the implications of excited states on atomic behavior and spectroscopy
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Students studying quantum mechanics, physicists interested in atomic structure, and educators teaching concepts related to electron binding energy in hydrogen atoms.

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Homework Statement



How much energy is required to remove an electron from a hydrogen atom in a state with n = 8?

Homework Equations



E = - (1 / 4pi*epsilon_0)(me^4/2(h-bar)^2)(1/n^2)

Where E is the total energy of the electron.

The Attempt at a Solution



I know that if you solve the above equation for the ground state (n = 1), the binding energy of the electron is equal to E, but I'm not so sure about excited states. Do I merely solve the above equation for n = 8, or is there something I'm missing?
 
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as you have said , to remove an electron from a hydrogen atom which is in a ground state , the least amount of energy you have to give is 13.6ev (note that En= -13.6/n^2) and n=1 in the ground state ...

so when the atom is at n=8, what is the least amount of energy you have to give it in order to remove the electron (can you see some kind of symmetry here ) ... :)
 
thebigstar25 said:
as you have said , to remove an electron from a hydrogen atom which is in a ground state , the least amount of energy you have to give is 13.6ev (note that En= -13.6/n^2) and n=1 in the ground state ...

so when the atom is at n=8, what is the least amount of energy you have to give it in order to remove the electron (can you see some kind of symmetry here ) ... :)

Well, the answer I got is 0.2124 eV...
 

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