From the fringe pattern of an empty Ir cell, the following wavenumbers were found for a seies of consecutive fringes: 3011.11 cm, 3058.12 cm, 3108.89 cm, and 3157.75cm, 3205.64cm, 3254.54 cm, 3303.26 cm. With a suitable graphical plot, calculate and express the answer to the correct significant figure the path length of the cell and its uncertainty
http://www.smarteam.com.tw/calcell.pdf
Another calculation site.
http://www.piketech.com/skin/fashion_mosaic_blue/application-pdfs/CalculatingPathlength-LiquidCells.pdf
Thank you to your suggestion, I have found that path length is 9.7574 mm. But do you know how to write correctly significant number and its uncertainty
To calculate the path length of the cell and its uncertainty, we can plot the wavenumbers against the fringe number and find the slope of the line.
1. Start by plotting the wavenumbers on the y-axis and the corresponding fringe number on the x-axis. The fringe number should be plotted as 1, 2, 3, etc. for the consecutive fringes.
Fringe Number (x-axis) = 1, 2, 3, 4, 5, 6, 7
Wavenumber (y-axis) = 3011.11, 3058.12, 3108.89, 3157.75, 3205.64, 3254.54, 3303.26
2. Once you have plotted the points, fit a straight line to the data. This can be done through the method of least squares, where you minimize the sum of the squared differences between the data points and the line.
3. Determine the slope of the line, which represents the change in wavenumber per unit change in fringe number. This slope corresponds to the reciprocal of the path length of the cell, expressed in cm^-1.
4. Finally, calculate the uncertainty of the slope. This is done by determining the vertical distance of each data point from the straight line and calculating the standard deviation of these vertical distances. The uncertainty of the path length is equal to the uncertainty of the slope, expressed in cm^-1.
5. To convert the path length from cm^-1 to cm, take the reciprocal of the slope. The uncertainty in cm can be obtained by taking the reciprocal of the uncertainty in cm^-1.
6. Express the final answer to the appropriate significant figures, based on the least accurate number in the data.
Note: The specific method for fitting the straight line and calculating the uncertainty may depend on the software or method used for the analysis.