The purpose of this lab is to use four different colored LEDs to arrive at a value for Plank's constant. The lab setup will be similar to the spectral line lab. The LED light will be viewed through a diffraction grating of 300 slits/cm that is 191.5 cm away. The spectral line will be viewed some distance away from the light source. Furthermore, voltage across the LED will be measured. The angle will be determined with the tangent inverse. With the Angle determined then the diffraction equation can be used to determine wavelength. Once wavelength and voltage is obtained for every LED, then a plot will be made of voltage vs. 1/(wavelength).
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| Diffraction Equation |
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| Part of the lab setup. The LED can been seen here. |
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| The setup from the point of view from the diffraction grating. |
Data and Interpolation:
| LED | d (cm) | Uncertainty (cm) | d - 2 (cm) | d + 2 (cm) |
| Blue | 28.4 | 2 | 26.4 | 30.4 |
| Green | 31.6 | 2 | 29.6 | 33.6 |
| Yellow | 33.9 | 2 | 31.9 | 35.9 |
| Red | 36.3 | 2 | 34.3 | 38.3 |
| LED | Theta (degrees) | Propagated Uncertainty | Theta Min (degrees) | Theta Max (degrees) |
| Blue | 0.14722975 | 0.010203 | 0.13699549 | 0.15743304 |
| Green | 0.16353933 | 0.01015 | 0.15335557 | 0.17368897 |
| Yellow | 0.17520836 | 0.010108 | 0.165064 | 0.18531642 |
| Red | 0.18733351 | 0.010062 | 0.17723294 | 0.19739556 |
| LED | Wavelength (nm) | Wavelength Uncertainty | Wavelength Min (nm) | Wavelength Max (nm) |
| Blue | 488.994741 | 33.8 | 455.194741 | 522.794741 |
| Green | 542.704407 | 33.5 | 509.204407 | 576.204407 |
| Yellow | 581.044372 | 33.3 | 547.744372 | 614.344372 |
| Red | 620.799083 | 33.1 | 587.699083 | 653.899083 |
| LED | 1/Wavelength (1/nm) | Voltage (v) |
| Blue | 0.002045012 | 2.59 |
| Green | 0.001842624 | 2.46 |
| Yellow | 0.001721039 | 1.88 |
| Red | 0.001610827 | 1.81 |
With the data interpolated and the plot made, the value for the slope came out to be 4770 v*nm. By dividing by the value for the speed of light and then multiplying by the charge of the electron, the experimental value for plank's constant came out to be 2.544*10^(-33). Despite the value coming close to the actual value of plank's constant, the percent difference is 283%. The uncertainty propagated to a large difference in the plot. The small angle approximation is also of a small concern for the diffraction equation due to the angles. It is also worth mentioning that if the linear fit was taken to the extreme uncertainty, that fit would yield a shallower slope. This would result in a smaller percent difference.
To further address the lab, the colors that seemed to deviate the most were red and blue. This is likely due to the energies associated with those wavelengths. The voltage increased with the energy of the LED wavelength I.E. red had the lowest voltage where blue had the highest voltage. The non primary color LEDs seemed to be a bit blurry between spectral lines. This is due to those LEDs utilizing primary colors to exhibit tertiary colors.