CHE 3200
ATOMIC SPECTRA
2015
OBJECTIVE :
(a) To measure the angular positions of the 7 lines of the spectrum of helium gas with a
spectrometer.
(b) To construct a calibration curve for the spectrometer using the known wavelength of the 7
lines of the helium spectrum.
(c) To determine the wavelength of the 3 lines of the spectrum of deuterium gas using the
spectrometer and the calibration curve.
(d) To determine the Rydberg constant RD for deuterium.
(e) To determine the error of RD .
(f) To find the wavelenths of the spectral lines of the atomic spectrum of an unknown gas .
BACKGROUND :
Read :
Chapter 1 ofJames E. House, Fundamentals of Quantum Chemistry
The following quantities will be used:
Z = nuclear charge number
me = mass of one electron
mN = mass of the nucleus
m=
me mN
= reduced mass
me + mN
e = elementary charge
h= Planck’s constant
 = h/2
n = principal quantum number = 1, 2, 3, ……
c = speed of light
~ =  /c = wavenumber
RH = Rydberg constant for hydrogen (1H)
RD = Rydberg constant for deuterium (2H)
The energies of hydrogen-like “atoms” are
En =
-Z 2 2p 2me 4 1
h2
n2
En = - R hc
with
R=
(1)
1
n2
(2)
Z 2 2p 2 m e 4
h 3c
(3)
using these formulas one arrives at
1
4
~  R H  
1 

n2 
1
for the wavenumbers ~ of the lines in the Balmer Series of hydrogen when n  2
Similarly for deuterium :
æ1 1 ö
÷
è 4 n2 ø
n = RD ç since
 = c
(4)
it follows that
n 2 - 4)
æ1 1 ö
(
= RD ç - 2 ÷ = RD
è4 n ø
l
4n 2
1
and
l=
4
n2
R D ( n 2 - 4)
(5)
(6)
therefore a graph of  versus n2/(n2 – 4) should give a straight line with the slope
m = 4/RD
PROCEDURE :
1.
Use the prism spectrometer (with the prism replaced by a diffraction grating) to record the
angular positions (in degrees) of the 7 lines in the atomic emission spectrum of helium.
Note : If you want extra credit, you could try to use a compact disk instead of the diffraction
grating. But you need to talk to me before you start. Extra credit is only available if you can make it
work in such a way that next year’s students can use it.
2. Record the atomic spectra (using scale readings in degrees) of
(a) deuterium (be sure to record all three lines).
(b) an unknown gas
ANALYSIS :
1. Assign the following wavelengths to the He lines:
447.1 nm, 471.3 nm, 492.2 nm, 501.6 nm, 587.6 nm, 667.8 nm, 706.5 nm
2. Construct a calibration curve for your spectrometer by graphing (He) in nm on the y-axis
versus scale reading in degrees on the x-axis. Make sure to allow enough room on this graph
for lines which may lie outside the wavelength range of your He lines. This should be done
using an Excel spreadsheet. Include a trendline and the equation of the trendline.
3. Use your calibration curve to assign wavelengths to all the recorded lines of deuterium
4. Determine the Rydberg constant of deuterium the following way:
Graph the wavelengths of deuterium (measured by you) versus n2/(n2 – 4) where n is the principal
quantum number of the upper level for that particular transition (equation 6).
Use Excel and LINEST to calculate m, b, e (m) , e (b) , e (y)
5.
6.
7.
8.
Calculate RD the Rydberg constant for deuterium from the slope.
Calculate the error in RD using the error in the slope.
Use the calibration curve to assign wavelengths to all lines of the spectrum of the unknown gas.
Try to determine the identity of the unknown gas.
2