For the Lab Report on the Toy Phosphorescence
 
Never present the results of a least-squares fit without an accompanying graph; the fit function should be graphed as a line and the experimental data should be plotted as individual points.  Never copy the entire output of an Excel regression into a Word document without editing it to remove the unneeded statistics.  You are better off formating the results in Word as a Word table, or creating a new Table in Word.  All tables must conform to ACS style: no vertical rules!
1) Plot the Intensity (voltage) vs time. This is your RAW DATA. It is NOT necessary to print out each data point in a boring list of numbers.  You may plot the voltages as positive numbers if your wish.  If you record data for several different colored toys, plot the several sets of data on ONE chart to save space and to make comparison easy.
2) Determine the order of the light decay. You may remember from kinetics in General Chemistry that if the decay is 1st order, a plot of ln I vs. time will be linear, and if the decay is 2nd order, a plot of 1/I vs time will be linear. Display both types of graphs, and decide based on the graphs which is the best. (Place different colored toys on one chart.)  Don't be surprised if the graphs don't appear to be very straight; the log or reciprocal data probably will not be linear because there is a nonzero background; that is, the photodiode gives a small signal even when no light hits it.  You can apply a background correction so that the data approach zero at infinite time--just subtract the final intensity from the rest of the intensity data, then redo the ln I and 1/I plots to see if the background correction improves the linearity of the graph.  After you do the background correction, graph the data again. Choose one color of toy and try fitting the corrected data to ln I vs time and 1/I vs time. Make a table comparing the two fits.  Which order is gives the straighter line?
 
 
3) Use Solver to fit the RAW DATA to a 1st order decay curve. Repeat for a 2nd order decay curve. Do the best solver fits yield the same rate constants as the "linearized" fits? Again, which order of decay produces better fits? Make a table for comparison; be sure to include the sum of square errors in your table!

The usual kinetics equations for first and second order reactions are
 

But don't bother to use these equations; they won't work very well.   These equations are derived on the assumption that the light intensity (like a reactant concentration) will approach zero at infinite time.  The signal from your photodiode does not approach zero; therefore, you will find that your nonlinear fits will be vastly improved if you include a term for the background signal:

You could subtract the background from all the data as suggested in part 2, but it is actually more elegant to let the nonlinear fit determine the best value of the background correction.  Chances are that your last data points aren't very good guesses for the true background voltage.  Solver will do a better job of figuring out what that value should be.  Solver should optimize three parameters, I0, Iback, and k, the rate constant.

Which order gives the better fit (Smaller sum of the squared errors)?  Place your results in a table.  Be sure to show a graph of at least one colored toy's data and the best Solver 1st order and 2nd order fits to the data.

4)  The data for the different colored toys should exhibit the same decay order.  However, they may not have the same rate constant.  Be sure to compare the rate constants for the different toys: are they same with in experimental error?
 

5) Search the Internet for information about the phosphorescence of glow-in-the-dark toys. If you have some success on the Internet and can formulate some specific questions for Chemical Abstracts, then go ahead and use STNEASY. What chemical or chemicals are responsible. What is the mechanism for the storage and regeneration of light? Have other people measured the light decay--if so, what did they observe? How does the analysis of your light decay data support or contradict the proposed mechanisms for light storage and regeneration?
 
 
All plots should be placed directly into the Word document as close as possible to the text that refers to the plot. Be careful when pasting plots from EXCEL; sometimes the plots take up a lot of disk space, to the point where you can't fit the Word document on to one floppy.  Press CTRL-SHFT-F9 after you paste a chart to prevent this.  All tables should be made in Word and must conform to the ACS style: no vertical lines! A final suggestion: write your abstract after you have written everything else.