[bamoida2]

Hello I'm preparing for exams at the moment.

I came across this question and have absolutely no idea how to even approach the problem!

Problem:

a)
A sample got analyzed via AAS (using a hollow cathode lamp) and shows an Absorbance of 2.0.

What would the absorbance be if you used a continuum-source with a monochromator with a bandwidth of 2nm. (for simplicity assume that the band profile is rectangular)

b)

If the detector noise was σ=2*10^-5 and the concentration of your sample was 0.001 mol/L for the previous example, what would be the detection limit using i.)a hollow cathode lamp ii.)a continuum-source (same as above).

[Arkcon]

Well, I'm not sure of an answer myself, and I wonder if this problem is solvable.  But, since you need it for an exam, we should try to take a stab at it.

You're asked to compare the output of a 2 nm monochromater applied to a continuous light source with the output of a hollow cathode lamp.  I'm not sure how monochromatic a hollow cathode lamp is, or how much bandpass it can have.  But try doing the math with a 1 nm monochromater, or a worse monochromater, say 3 or 5 nm.  Then, you will at least have practiced the math required, and you'll be ready when you have better facts.

[bamoida2]

Well this question was asked in that exact same way (in German) in some previous exams (people are collecting those as this exam is one of the worst, if not the worst in my BS at my university and it gets worse by the professor trying to come up with all new questions so people who collect the questions don't have an advantage. And so far noone was able to solve it. I'm not sure if it even solvable myself (apparently the professor explained it to someone after reviewing a test with a student(but he didn't understand it at all), maybe the professor thinks about a way to solve it that is wrong?).

HCL lamps bandwiths are approx 10^-3 to 10^-4 nm.

Thanks for your advice I'll practice calculating the resolutions of monochromators/gratings

Calculating the theoretical resolutions etc are quite easy, but I have no idea how to convert the real value of a HCL experiment to the theoretical one if you used a CS lamp instead.

It just seems to me there is at least one more parameter missing.

[Arkcon]

HCL lamps bandwiths are approx 10^-3 to 10^-4 nm.

Yikes. That is tight.  From Wikipedia, HCL's can give a number of lines, depending on the metal, or they can give lines from the inert gas they contain.  What's missing is the intensity of the continuous source and the HCL.

[bamoida2]

Ok, I guess if we assume that the bandwith of the HCL is 10^^-3nm and the intensities are the same it should be possible to calculate, right?


10^^-3/2000 = for 2000 bandwidths of 10^-3 there is only one that absorbs light.

Can we now just do A= 2/2000?

I tried calculating it trough the transmission but I got an absorbance of 1 which doesn't make sense at all.

an absorbance of 0.001 would mean that only 0.0023% of the light is absorbed which makes sense, but I have no idea if that is correct.


for b)

I guess we have to create a calibration line that goes trough (0|0) and another line that is y=10σ (Kaiser LOQ).  The LOQ should be where those lines intersect.