The Spectrum of the Hydrogen Atom

Here are some quick notes on the error analysis for this lab. The write-up in the manual implies that you will be able to make to better than a part in a thousand. Perhaps. What I'd like you to do this in this lab is apply what you know about error analysis to determine just what your errors are in extracting the integers in the Balmer formula.

One source of error is the difference (if any) in angle when you measure the location of the He line on both the right side and the left side of the grating. If these two numbers agree, then you would say you have determined to better than the precision of the apparatus. More typically, you will get two different values, call them and . If these are random errors, then an estimate for the error comes from the standard formula for N random measurements



for the case N=2 (in this result, )

Have your lab partner make the same measurement of these angles. If his/her results agree with yours, then there is probably a systematic error in determining the angle between the left and right hand sides of the apparatus. There is no trivial method by which to determine the actual magnitude of such systematics, but taking is good enough here.

Propagating the errors measured on the angles into the values of is tedious but straightforward. (Don't forget to propagate the error both on the angle for a given line, and on the value of d obtained from the He calibration.) I used a spreadsheet to organize my calculation, and it wasn't too bad. Doing so I obtained values such as



This is what I would call 'reasonable', that is, the value is an integer 'at the 2-sigma level',