Today's experiment can seem a bit confusing because it demonstrates two separate phenomena, emission spectra and diffraction of light.     To keep frm getting lost in the lab, you must become very comforable with these two concepts.   Why?  Because the apparatus will show them both superimposed on top of one another. 

Key Concepts:

Emission Spectra:  The set of light wavelengths that emerge from an excited gas.





We will observe the light that emerges from excited hydrogen gas.  Everyone knows that all colors mixed together gives you the color white.  The sun is a good example this.    Our excitged hydrogen gas, won't have all of the colors in it that the sun does, but only a few.   Every gas will give a different spectra. 

Applet

Light is a wave, and the difference between two light waves of different color, is in the spacing between their crests.  This spacing is called the wavelength and its symbol is the greek letter lamda ()   .    



Hydrogen, like all atoms has electrons that can populate only discrete energy levels.      When an gets excited, it can jump to a higher level than where it is.     It usually at the high energy level for a tiny amount of time, and when the electron goes from a this higher "excited" energy level (k) to a lower energy level (j) , the difference in energy gets emitted as a little packet of light (a photon) who's wavelength is completely determined by the two energy level indiceds.    The wavelength of the emitted light corresponding to the transition from k to j is given by,
 

where R is a constant known as the Rydberg, equal to  .

Our apparatus can only observe transitions with j=2.     The index k can take on any value greater than j=2, (3,4,5,...) since it represents higher energy levels than j.    

Each combination of  j and k corresponds to a different wavelength ()and thus, a different color.  The set of all wavelengths that have j=2 are called the Balmer series.  



Diffraction:  The scattering of a single beam of light into multiple beams, when it hits an objects that has dimensions about the size of it's own wavelength.




O.K.      So our electrically-excited hydrogen lamp will consist of a bunch of selected colors.    But if we just look at the lamp with our eyes,  these colors will all be mixed together and we'll just see a pinkish haze.
  
In order to separate the colors into the discrete transitions that make up this pinkish haze,  we will focus some of this light into a little slide called a diffraction grating.     The grating is nothing more than a bunch of tiny parallel lines, just like the gratings on a jail cell.      But the dimensions of the grating are similar in size to the wavelengths that we're shooting through it.     

And whenever waves interact with objects that are about as big as they are, a special kind of scattering occurs known as diffraction.   

A single beam of light will scatter off of the grating and emerge as many beams with indices m = 0,1,2,3,,,,.       The outgoing beam with m = 0 is called the "zeroth order" beam and it goes straight through.     The beam with m=1 is called the "first-order" beam and the beam with m=2 is called the "second order" beam.

All of these higher orders beams have the same color (wavelength) as the incident beam.

Each order m refers to a pair of diffracted beams that emerge from the grating at angles  from the initial beam's direction.

The directions of the beams diffracted from the initial beam of wavelength is given by the relation,