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 mass*of 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%).