Question

The Problem: Inconsistencies between the measured and true values of mercury's spectra light wavelengths emitted following a laboratory experiment.

What I Know: The experiment conducted was viewing the colors and distances of emitted lights, through a grating, from a sample of mercury in a transformer. Purple, green, and orange were determined correctly to be the spectral light colors of mercury and the wavelengths for each must be found in centimeters. The formula λ=dsin(arctan((x/y))�=�sin⁡(arctan⁡((�/�)) is required, where d=1/5.3×103�=1/5.3×103 with regards to the constant distance between the grating grooves, x=(x1+x2)/2�=(�1+�2)/2 with regards to the average x-axis length from the transformer, and y=99.9�=99.9 with regards to the constant y-axis length from the transformer.

Failed Calculation: The x-axis length averages were determined to be 9.25, 11.63, and 12.75 centimeters for purple, green, and orange correspondingly. After plugging the values into the formula, it resulted in wavelengths of 1.74⋅10−51.74⋅10−5, 2.18⋅10−52.18⋅10−5, and 2.39⋅10−52.39⋅10−5 centimeters. However, the true wavelengths are 4.35⋅10−54.35⋅10−5, 5.46⋅10−55.46⋅10−5, and 5.77⋅10−55.77⋅10−5 centimeters.

Attempted Fixes: I have already checked the data collected alongside formula input, and the formulas are what must be used when solving for the wavelengths.

With a percent error of about 60%, I do not understand how I am finding mercury's wavelengths wrong with the given formulas or what I am missing. Any help would be much appreciated.

Answer 1

There is a discrepancy between measured and true wavelengths in a mercury spectral lines experiment. The issue lies in the formula application and measurement accuracy. The correct approach requires a reassessment of experimental values and formula use.

Step-by-step explanation:

The issue observed seems to be related to the calculation of the wavelengths of light emitted by mercury vapors using a diffraction grating in a physics laboratory experiment. The student has encountered discrepancies between measured and true values and is trying to understand the source of these inconsistencies.

To calculate the wavelengths, the formula being applied is λ=dsin(arctan((x/y))), with d representing the distance between the grating grooves, x as the average x-axis length, and y as the constant y-axis length. To correct the observed percent error of about 60%, it is necessary to reassess the experimental setup's constants, measurements, and the implementation of the formula.