Defining Variables for Data Analysis in a Lab Experiment

[CptXray]

Homework Statement

Hello, I have a problem with my data analysis from my lab. My goal is to find drift velocity of the electron and it's diffusion coefficient. The experiment looked like this: I've measured the time difference between signals on two gaseous detectors. The source of the signal were $\alpha$ particles from radioactive element inside the measurement system. Alpha particles ionize the gas inside chamber and then electrons are accelerated in a constant potential etc. Everything went fine until professor said that full width at half maximum should be $\sigma = A \cdot t^{3/2} + \sigma_{0}$ and it does match my data:

Homework Equations

The problem is that in general $\sigma = \sqrt{2Dt}$.

The Attempt at a Solution

I don't know to go form $\sqrt{2Dt}$ to $A\cdot t^{3/2} + \sigma_{0}$, because the last thing to do is finding diffusion coefficient. I'd appreciate any help and tips.

 

[haruspex]

Homework Statement

Hello, I have a problem with my data analysis from my lab. My goal is to find drift velocity of the electron and it's diffusion coefficient. The experiment looked like this: I've measured the time difference between signals on two gaseous detectors. The source of the signal were $\alpha$ particles from radioactive element inside the measurement system. Alpha particles ionize the gas inside chamber and then electrons are accelerated in a constant potential etc. Everything went fine until professor said that full width at half maximum should be $\sigma = A \cdot t^{3/2} + \sigma_{0}$ and it does match my data:View attachment 239773

Homework Equations

The problem is that in general $\sigma = \sqrt{2Dt}$.

The Attempt at a Solution

I don't know to go form $\sqrt{2Dt}$ to $A\cdot t^{3/2} + \sigma_{0}$, because the last thing to do is finding diffusion coefficient. I'd appreciate any help and tips.

Please define all your variables.