Lab 4
Hydrogen Spectrum
Bill Chun Wai Hung
Nimish Kumar
Binh An
Friday Section
7 May 2004
Data:
The experimental results are as the followings.
Table 1. Hydrogen Spectrum
Wave Width(nm) |
Wavelength(nm) |
% Intensity |
47.320 |
701.975 |
1.00000 |
36.736 |
517.754 |
0.09847 |
0.760 |
465.071 |
0.06370 |
0.357 |
430.430 |
0.05793 |
Table 2. Deuterium Spectrum
Wave Width(nm) |
Wavelength (nm) |
% Intensity |
44.632 |
700.884 |
1.00000 |
38.759 |
519.655 |
0.09951 |
1.792 |
463.021 |
0.06052 |
1.220 |
431.342 |
0.05843 |
Calculation:
where
if the mass of
electron is 9.11 x 10-31 kg,
mass of hydrogen is 1.67 x 10-27 kg, and mass of
deuterium is twice of that of hydrogen, which is 1.67 x 10-27
kg x 2 = 3.34 x10-27.
of hydrogen
of deuterium
Wavelength (nm) |
Relative Intensity |
Transition |
383.5384 |
5 |
9->2 |
388.9049 |
6 |
8->2 |
397.0072 |
8 |
7->2 |
410.174 |
15 |
6->2 |
434.047 |
30 |
5->2 |
286.133 |
80 |
4->2 |
656.272 |
120 |
3->2 |
656.2852 |
180 |
3->2 |
Conclusion by Bill Chun Wai Hung:
1. Principles and Results
By measuring the radiation emitted from
hydrogen and deuterium, the energy level of hydrogen and deuterium can be
determined. This is because the energy levels of hydrogen and deuterium are
proportional to the intensities of emission of these energy levels.
By using the computer and the light
sensor, graphs of Intensity versus Wavelength of hydrogen and deuterium can be
plotted.
From the graph, information like the
wavelength for certain wavelength, the wave width, and the percentage
intensities can be obtained. The results are presented in Table 1 (Hydrogen)
and Table 2(Deuterium).
Table 1. Hydrogen Spectrum
Wave Width(nm) |
Wavelength(nm) |
% Intensity |
47.320 |
701.975 |
1.00000 |
36.736 |
517.754 |
0.09847 |
0.760 |
465.071 |
0.06370 |
0.357 |
430.430 |
0.05793 |
Table 2. Deuterium Spectrum
Wave Width(nm) |
Wavelength(nm) |
% Intensity |
44.632 |
700.884 |
1.00000 |
38.759 |
519.655 |
0.09951 |
1.792 |
463.021 |
0.06052 |
1.220 |
431.342 |
0.05843 |
By comparing the
results of hydrogen and deuterium, the results suggest that the radiation
pattern of hydrogen and deuterium are the same or very similar.
The experimental results suggested the
radiation pattern of hydrogen and deuterium are very similar is consistent with
the theoretical assumption.
Since
where
and
of hydrogen
of deuterium
the value of the reduced mass of hydrogen is very close to the reduced mass of deuterium. This is because the mass of electron is significantly smaller than that of hydrogen or deuterium (about 1:2000). Therefore, the small mass of electron does not affect the reduced mass of hydrogen or deuterium very much.
Since the
reduced massof hydrogen and deuterium are close, and the energy equation
contains all constants (, k, e, h) except, so the energy pattern of hydrogen and deuterium would be
predicted to be very similar. The assumption of the energy pattern from the
equation is consistent with the experimental results obtained from the actual
experiment.
2. Error Analysis
The laboratory in which the experiment is performed has light sources
other than the light from hydrogen tube or the deuterium tube. The additional
unwanted light contributes to the radiation pattern generated by the computer.
The additional unwanted light gives noise and other interfering factors to the
final plotting of the radiation graphs.
The value of the percentage intensity, wavelength, and the wave widths
are approximated by placing the hair cross of the computer to the
computer-generated graph. Since the mouse is not moving very smoothly, and the
hair cross actually jumps with certain increments, the value obtained by
placing the hair cross on the graph may be off the true value by ¡À 1 unit (of
wavelength = nm, or of % intensity = 1%).