Physics307L:People/Dougherty/Notebook/071022

Balmer Series
http://www-hep.phys.unm.edu/%7Egold/phys307L/manual.pdf

p27-30

http://en.wikipedia.org/wiki/Balmer_series

According to the manual i calibrated the apparatus with the mercury spectrum. i first found the right measurement for the red line that shows up in the spectrum. by fixing the screw drive to that measurement i could then fix the prism so the actual red line of the spectrum fell on the cross hairs in the viewing lens. this way the red line of the spectrum fell exactly on the right wavelength of the screw drive. and then moving the screw drive to the second wavelength, i could see the blue/green line fell on the same measurement as in the manual.

also in the manual, they specifically expressed turning the screw drive in only one direction. this is because there could be dead spots if turned the opposite way. dead spots meaning if you reverse the direction, you might turn the screw drive a fraction of an inch or so before the spectrum itself actually starts moving. for this reason i decided to take 2 measurements. one turning the screw drive completely counter-clockwise and moving it along the spectrum, and then turning it completely clockwise and moving it the other way along the spectrum. this way i could minimize any error in the movement of the screw drive.

Data
Hydrogen

turned screw drive all the way counter-clockwise

turned screw drive all the way clockwise

Deuterium

turned screw drive all the way counter-clockwise

turned screw drive all the way clockwise

Data Analysis

 * $$\frac{1}{\lambda} = R_\mathrm{H}\left(\frac{1}{2^2} - \frac{1}{n^2}\right), n=3,4,5,...$$

For Balmer series the red line's atomic number, n, starts as 3 and moves up as the spectrum moves left. (blue/green = 4, violet = 5, and violet (faint) = 6.)

Hydrogen

counter-clockwise

clockwise

Deuterium

counter-clockwise

clockwise

R average
counter-clockwise

Hydrogen - R = 1.10001*10^7 m^-1

Deuterium - R = 1.10107*10^7 m^-1

clockwise

Hydrogen - R = 1.09815*10^7 m^-1

Deuterium - R = 1.09908*10^7 m^-1

Hydrogen
R = 1.099*10^7 m^-1

Deuterium
R = 1.100*10^7 m^-1

standard error of the mean


s = \sqrt{\frac{1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2} $$

Hydrogen = 16696.87738

Deuterium = 23383.54027


 * $$SE = \frac{s}{\sqrt{N}}

$$

Hydrogen SE = 5903.23761

Deuterium SE = 8267.329947

Final value of R
Hydrogen = 1.099*10^7 m^-1 +/- 5.903*10^3

Deuterium = 1.100*10^7 m^-1 +/- 8.267*10^3

error
$$%error= \frac{|Actual-Experimental|}{|Actual|}x100$$

actual value = 1.0967758*10^7 m^-1

Hydrogen e= 0.20%

Deuterium e= 0.29%