Physics Lab
The Hydrogen Spectrum and the Bohr Model
1
Introduction
In this lab, we use our grating spectrometer to make precise measurements of the wavelengths of the
spectral lines of Hydrogen. Using these, plus Balmer’s formula and the Bohr model, we can find the
Rydberg constant and the energy levels of the Hydrogen atom.
Procedure
Part I: Setting up the spectrometer
Follow the instructions for Parts I and II of the previous lab, “Grating Spectrometer,” with the
exception that we will use a Hydrogen spectrum tube, rather than Helium.
Part II: Collecting Data
Follow the instructions for Part III of the previous lab, with the exception that you should try to
observe all lines that are in the visible range of the spectrum, for m=1, m=2 and m=3. You should
be able to see clearly at least four lines; you may be able to see many more (with most of those in the
violet range of the spectrum). If you can not see any of the lines at any of the orders, be sure to note
that clearly in the data section of your report.
Analysis
1.
Calculate the average of your left and right angles for each line (a column for this is included
in the data table).
2.
Use the average angle, the order, and the grating spacing in the grating equation, to calculate
the wavelength in each case. (Note that you only have to show one such calculation, just show
results for the rest.)
3.
Average the wavelengths that you found for that line in the first order, the same line in the
second order, and the same line in the third order (where visible).
4.
Use Balmer’s formula, and your data, to calculate the Rydberg constant. Do this for each of
your spectral lines (the Hα, Hβ, Hγ, etc.). Then, find the average of your Rydberg constant
results.
5.
Calculate the Rydberg constant from fundamental quantities, as discussed in the text.
6.
Calculate the % error for your average from step 4, vs. the accepted value found in step 5.
Results
Give a table listing your calculated wavelengths from Analysis step 2 above, the average wavelength
from step 3, the Rydberg constants from step 4, the average Rydberg constant from your data from
step 4, the theoretical Rydberg constant from step 5, and the % error from step 6.
Questions
1.
Are the theoretical Balmer wavelengths consistent with your measured wavelengths? Why or
why not?
2.
Are you surprised by the accuracy of your results? Why or why not?
Physics Lab
3.
The Hydrogen Spectrum and the Bohr Model
2
Sketch an energy level diagram of the hydrogen atom with the various levels labeled with the
proper value of the quantum number n. Indicate on your diagram which transitions cause the
lines you observed in the Balmer series.
Reference Information:
(From: http://www.solarobserving.com/halpha.htm)
Color
Wavelength Relative
(nm)
Intensity
Transition
Name
Red
656.28
180
n=3 → n=2
Hα
Cyan
486.13
80
n=4 → n=2
Hβ
Blue-Violet
434.05
30
n=5 → n=2
Hγ
Violet
410.17
15
n=6 → n=2
Hδ
Violet
397.01
8
n=7 → n=2
Hε
Violet
388.90
6
n=8 → n=2
Hζ
Violet
383.54
5
n=9 → n=2
Hη
(Adapted from: http://hyperphysics.phy-astr.gsu.edu/hbase/hyde.html)
Physics Lab
The Hydrogen Spectrum and the Bohr Model
3
Data Table
Reference Angle (if necessary):___________
Color, Side
, Right
, Left
, Right
, Left
, Right
, Left
, Right
, Left
, Right
, Left
, Right
, Left
, Right
, Left
, Right
, Left
, Right
, Left
, Right
, Left
, Right
, Left
, Right
, Left
, Right
, Left
, Right
, Left
Brightness
Order (m)
Measured Angle
Difference Angle
(if necessary)
Average Angle