Wavelength of a gas lamp

Quantization of energy levels in atomic nuclei results in different colors of emission spectra for different elements. For example, this picture features a mecury gas lamp viewed through a diffraction grating.

It is clear that there are three spectral images formed to the right of the actual lamp. These three spectral images have colors corresponding to the wavelengths of photons emitted from mercury when one of its electrons is excited and then relaxes to a lower energy state.

Our experimental apparatus, as visible in the picture, consists of a 2 meter stick, and a meter stick arranged orthogonally on a table. The horizontal displacement of the spectral images can thus be converted into an angular relationship, or it can be left in units of length to solve for the wavelength of the light directly.

Similar to the CD diffraction experiment, the position of the spectral images and the spacing of the diffraction grating can be used to determine wavelength. The governing equation is:

λ = (D*d)/sqrt(L^2+D^2)
Where:
D = the horizontal distance of the image
d = the diffraction spacing
L = the distance between the diffraction grating and the gas lamp

This experimental setup yielded the following data for a hydrogen lamp placed in the same location:

position of image in cm:
1=48
2=54
3=74.5
uncertainty: .5cm


L = 2 meters
d = .000002 meters

This setup yields the following prediction for the wavelengths

1 = 466nm

2 = 523nm
3 = 698nm

Calibration of our apparatus against a white light, yielded a correction factor for our setup which included a systematic error of +37.7nm

When factored into the previous data, our final results are

1 = 428.3nm
2 = 485.3nm
3 = 660.3nm

when compared to the actual spectra for hydrogen:

1 = 434 nm
2 = 486 nm
3 = 656 nm

It appears our predictions are correct to within a single percent. This falls approximately in the same range as our uncertainty in horizontal position.