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Question

What energy photon is necessary to raise an electron in hydrogen from the n=1 to the n=3 energy level?


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Solution

Bohr's Model of a Hydrogen Atom

  • The Bohr model of hydrogen's atomic structure first accurately explained the radiation spectra of atomic hydrogen.
  • Bohr’s model of the hydrogen atom is based on three postulates.
  • An electron travels in a circular orbit around the nucleus.
  • In orbit, an electron's angular momentum is quantized.
  • A photon is emitted or absorbed whenever an electron's energy changes when it makes a quantum jump from one orbit to another.

Energy

  • The energy is as follows:

E=EfEi

  • E is the energy photon.
  • Ef is the final level energy.
  • Ei is the initial level energy.
  • Energy of nth excited state is, En=13.6n2.
  • The energy required to raise an electron in hydrogen from the n=1 to n=3 is as follows:

E=EfEi=-13.632--13.612=-1.51+13.6=12.1eV

  • The required energy is 12.1eV.

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