"So little done, so much to do"
Cecil Rhodes
(on the day of his death)

• All physical systems seek the lowest possible energy configuration.  The ground-state of the Hydrogen atom has the lowest possible energy of  this system.  We must supply energy to ionise the atom.  Therefore, left to their own devices, Hydrogen atoms will naturally prefer to be in their ground-state.

 What purpose do the other allowed energy levels serve ?  


If we provide enough energy to a Hydrogen atom in its ground-state we can excite it into one of the higher energy levels.  The source of the energy could be photons or via collisions with some other particles e.g. electrons.  In any event, the energy necessary to excite a Hydrogen atom to its first excited state (n=2) is exactly equal to the difference in energy between the ground-state and the first excited state (E₂ - E₁).  Only when this exact amount of energy is supplied will the atom be excited.


In search of its lowest energy configuration the Hydrogen atom in the first excited state will de-excite to the ground-state, by emitting a photon of energy exactly E₂ - E₁.  The de-excitation process is takes place in a fraction of a second.


If a large sample of Hydrogen atoms are excited, for example, by collision with electrons of suffcient energy, many of the excited states (n > 2) will be populated.  As these excited atoms de-excite they emit photons of specific energies which form the charactersitic atomic spectrum of Hydrogen.


• In the diagram below three "series" of transitions are shown,


• Lyman series:  n>2 levels de-exciting to the ground-state (n=1).  Lyman photons are in the UV region.
• Balmer series:  n>3 levels de-exciting to the n=2 level.  Balmer photons are in the visible light region.  The first 4 lines are shown in the spectrum as red, light blue,  blue and violet lines.
• Paschen series: n>4 levels de-exciting to the n=3 level.  Paschen photons are in the Infra-Red region.
  





• The wavelength of the photons in the Hydrogen spectrum is given by
  
  
  
  
  
  where R is the Rydberg constant, R = 1.097 x 10⁷ m^-1 (R = E₁/hc).  m is the principal quantum number of the final state.  n is the principal quantum number of the initial state,  n>m.  For example for the Balmer series of photons m = 2 and n takes on integer values 3 and over.


• The diagram below is an alternative representation of the origin of the Hydrogen spectrum, which also displays the different orbits of the energy levels.
  
  
  

   Supplementary Problems 

Why did the chicken cross the road ?
Wolfgang Pauli: "There already was a chicken on this side of the road."


 

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu