[Halogen876]

Hi,

I've been struggling with the foloowing question and I'd really appreciate some *delete me* Here is the question:

The bandwidth in chromatography could be described as the width (distance) bewteen the 2 inflection points on the peak (the points at which the slope is steepest). Assuming an ideal peak (Gaussian), show mathematically what this bandwidth would be in terms of s. At what height would this bandwidth be measured.

The answers are that the bandwidth would be 2s and the height at which this would be measured is DR=0.607h.

I think I understand where the 2s is coming from since that just implies going one standard deviation on either side of the midpoint of the peak but I can't figure out where the DR=0.607h is coming from. I know that DR=h·e^{[-(t-t_r)²]/(2s²)} but without knowing t and t_r, I'm not sure where to go with this from here...any help would be very much appreciated!

[Borek]

Somehow I feel like the good starting point would be to find the derivative.

Just an intuition, doesn't have to be right.

[mjc123]

Well, if it's one standard deviation either side of the midpoint, then |t-t_r| = s, so you just plug that into your formula.
But if you want to prove that the inflection points are at t_r±s, you need to take the derivative. Do you know how to find the inflection points of a curve?

[Halogen876]

Thank you to both of you. I see where you're coming from and I see that if I do just plug the absolute value of t-t_r in for s, that I will get the correct answer.

I understand that if I wanted to prove that that's where the inflection points are, I would need to do something more complicated like finding the derivative, but I don't think that's actually required for this question. I don't know how to find the inflection points but it's been a long time since I've done calculus and calculus isn't a prerequisite for the course that this question comes from so I don't think they actually require the answer to be that in-depth.

Thanks again to both of you - I really appreciate everything you've both done for me

[mjc123]

The question does say "show mathematically what the bandwidth would be", which suggests more than simply saying you know that for a Gaussian peak the inflection points are at peak ± s.
Inflection points occur where the second derivative is zero.

[Halogen876]

Ok, thank you.