Experiment 4: Spectrum of the Hydrogen Atom

April 24,2003

Kelsie Betsch, Sheereene Hussain and Carly LaCroix

Introduction:

Analyzing spectrum through the observation of spectral lines gives insight to the orbital configuration of the electrons of the particular element. In the case of hydrogen, these lines are particularly simple, because of the singular electron orbiting around the single proton. In order to view these lines, a high voltage is run through a glass tube containing the intended gas at a relatively low pressure. These normally diatomic gases are then dissociated into atoms by the increased incidence of electron impact. The result is many electronically excited atoms formed by the collisions, which then undergo a number of transitions to lower excited states. The energy that is released from these transitions appears in the form of spectral lines. With each lines’ wavelength corresponding to the relative energy emitted by the released photon. In the following lab, these lines were observed for various elements with the use of the UV-Vis spectrometer in order to capture Balmer series lines.

Procedure:

The procedure was that which is outlined in Experiment 40 of Shoemaker, and Garland. Spectra were observed for Hydrogen and Helium.  Specifically, the receptor probe (or the right side) was unscrewed from the holder and held at varying positions relative to the gas lamps.  All lights in the room were turned off so no ambient light would interfere with the desired spectra.  While probe position was varied, one person watched the spectra collected on the computer to make sure that all peaks were to scale.  Peak positions and intensities were identified using software.

Results:

The following are the captured UV-Vis spectra and the tables of results.
 
 

Fig 1 - Hydrogen UV-Vis spectrum
 
 

Table 1:
 
Hydrogen 
Balmer Series
Wavelength (nm)
 n (1/cm)
n1 values
calc n values
R values
434.265
23027.414
5
23032.2919
Rexp
109755.00
486.27
20564.707
4
20564.5463
Rvac-exp
109725.37
656.855
15224.06
3
15232.9973
Rvac-known
109677.58

Link to Excel files
 
 

Chart I - H Balmer series plot
 
 
 

Fig 2 - Helium UV-Vis spectrum
 
 

Table 2:
 
Helium 
Observed wavelengths (nm)
Accepted wavelengths (nm)
Refined Intensity
Accepted relative intensity
389.07
388.86
1319
500
447.22
447.17
360
25
471.26
471.31
85
30
492.38
492.19
169
20
501.53
501.57
613
100
586.81
587.56
3987
500
667.52
667.81
1460
100
706.29
706.52
2181
200
727.77
728.14
182
50

From the data observed with Hydrogen, the calculated Rydberg constant was relatively close to the accepted value, once vacuum considerations were taken. The remaining error between the experimental value and the known value could be due to the resolution of the spectrometer, and peak analysis.

The observation of Helium provided data that was consistent with the accepted values. In comparing, peak intensity, the relative intensities of the accepted values followed a similar trend as that observed in the experiment.

Using the formula (1),

n = R [ (1/n22) - (1/n12) ] (1)

and letting n2=1 and n1=2, the corresponding wavelength is 121.5 nm which lies in the ultraviolet region of the electromagnetic spectrum. Then using the same procedure with n2=3 and n1=4, the corresponding wavelength is 0.001876 mm which lies in the heart of the infrared region. The reason for decreasing intensity of the Balmer series as wavelength decreases is because these shorter wavelengths correspond to higher energy shifts. The population in the higher excited states is decidedly smaller than in those closer to the ground state energy.

Conclusion:

The UV-Vis spectrometer was used to capture spectra of several different molecules, which provided ample opportunity to become proficient in the use of this instrument. The experimental resulted corresponded with the excepted values, which reinforced the theory of limited energy transitions, as well as the quantization of energy theory. Overall, no significant obstacles were encountered in the experiment, however the use of elements with lower numbers of electrons provided spectra which was easily interpreted, contrary to the complicated spectra obtained from many electron atoms.
 

References:

  1. Carl W. Garland, Joseph W. Nibler, and David P. Shoemaker. Experiment 40: Spectrum of the Hydrogen Atom. Experiments in Physical Chemistry. 5th Edition. McGraw Hill. © 1996. pgs. 482-489.
  2. Peter Atkins and Julio de Paula. Physical Chemistry. 7th edition. Oxford University Press. (c) 2002.
  3. NIST Atomic Spectra Database.  Online date accessed: 27 April 2003.  Available: http://physics.nist.gov/cgi-bin/AtData/main_asd

 
 
 
 
 
 

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