Spectra

 

Follow the instructions from the guide sheet.

In preparation, go through the regular lab. experiment (i.e. your notebook report) and make sure you know what you are supposed to do at the test.
At the Lab. test you will not have to go through the calibration process (with the Na spectral source).

As soon as you get to the apparatus make sure you see the cross hairs, and that you are able to focus the spectrometer properly.
Center your spectrometer on the source to get the maximum brightness.
Adjust the width of the entrance slit if necessary (as you may recall, a narrow slit allows you to see only the brightest lines...)

To get the measurements use, as recommended in the guide sheet, the brightest lines.

If possible, drop by to the lab the week before the test for a bit of extra training in the identification of those lines.
The practice shows that this is the main challenge: getting the right correspondence between the lines and 's.

The Graph

Use most of the area of the graph paper.
Hopefully, this will allow you to display the error bars for at least one of the variables
(independent [ 1/(-0) ] or/and dependent [ y ] )

You expect to get a straight line of best fit, and determine the slope m right from (and on) the graph.

As already noted, the biggest challenge is to get the right identification of the lines. Make sure you don't add extra-challenge by misplacing the points on the graph.

Quote the units throughout.
For the units of y you have to write "arbitrary units".
For the units of 1/(-0) you have nm-1 (perhaps with a multiplier, since you may want to quote numbers like 0.003 nm-1 as (3 × 10-3 nm-1).

The (reading) errors

You are measuring the position of lines (given by y) for various .
As you may remember, the only reading errors are in y and 0.
The error in y adds up from
- a reading error on the vernier's scale: about 0.02 units (the repeatability error - read the description in the Lab. Manual, pg. 99, for details)
and, maybe,
- some human error - in case you don't get the center of the lines correctly :-) . Of course, this second error can be minimized - just be careful.

The value of 0 is written on the top of the spectrometer; the error is typically 0.4 - 2 nm.
For you are advised to assume no errors at all.
Therefore, the error calculus is greatly simplified.

The error bars for y are most probably too small to be displayed.
Example:  The brightest lines show up for y in the interval ( 6 ... 16); hence, the lenght of the axis for y is 10 units.
Assuming you take 200mm for 10 units of y, then 1mm on the graph paper corresponds to 10/200 = 0.05 units of y.
Since the error in y is about (± 0.02) units, then the error bar in y is only ( 1mm × 0.02/0.05 ) = ± 0.4mm which is hardly displayable.
It seems that you cannot see the error bars for the y...

For the horizontal axis, on which you plot 1/(-0), you need to do some calculus.
For a fast-track error estimate it is probably a good idea to calculate the error in the smallest and largest value of 1/(-0) and then interpolate the errors for the remaining points (if you have time, calculate them individually - it's not that hard).

In case you are out of time, leave this error calculation aside.
It might happen that the spread of your points is so wide that plotting the reading errors (and hence the error bars) are of no help or/and significance.
On the other hand, if this wide spread happens to you, then better check again how you identified the lines (the correspondence of with y).

Check the plots you have done for the regular lab. experiment. See how big the error bars are. You should get the same at the lab. test.
Expectations:  if the error in 0 si 2nm then the error bars should be visible (at least for some of the 1/(-0) values.
If the error in 0 is 0.4nm or so, then you will not see the error bars :-)

Error in the slope

The error in m  has to be retrieved using the minimum and maximum slope fit lines (see Lab. Manual, pp. 133-140 for details on fitting techniques).
Quote m  with the right units and the right number of significant digits.

Note: using previously recorded data (from a notebook) it took me about 15 min. to:
- draw the table (properly labeled) and copy the data
- calculate 1/(-0) (a column in the table)
- calculate the error in 1/(-0) (a column in the table)
- design the graph (and draw the axes, put the labels, units)
- plot 5 data points (with no error bars, since they were too small to be displayed)
- draw the best fit line
- retrieve the slope m from the graph
  I couldn't get b (see fit formula) because my horizontal axis started at 2× 10-3 nm-1, not at 0.
- estimate a reading error for the slope
(I didn't use the min-max slope lines, since the points were laying very nice on the best fit line - no room for swinging :-).
Instead, I considered that there is a 0.5% relative error in the slope due to reading errors (of the run and rise) from the graph (see the Common recommendations page for more details on how to get the error in the slope).

Moral: you have to train yourself, to make sure you can do the analysis smoothly.

Conclusion

Write down again you main result
(the value of the slope, with the right units and also the error, if any).
You may want to comment on the quality of the fit to a straight line of your data (good/bad/...).

 

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Last modified: July 02, 2003
© Sorin Codoban, 2003