Calculation of silver nanoparticle size using Mie Theory

I have synthesized silver nano-particles and I wish to determine the approximate particle size using the wavelength that was most absorbed according to its absorption spectrum.


I find out that Mie theory provides a good approximation for this, (Eq 4 in [this paper](https://www.researchgate.net/profile/Yuriy_Gnatenko2/post/Can_anyone_explain_how_to_calculate_particle_size_from_Uv-Vis_spectra/attachment/59d6322ac49f478072ea168b/AS:273630724853779@1442250056479/download/Ag_nanoparticle+size.pdf)). However, I am clueless as to how to use the equation. In other words, how should I use the $\lambda\_{max}$ obtained through the experiment in the provided equation?




Plug it in to the math equation
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Ok, so we have this equation: $γ(R)=γ\_0+(Av\_f)/R$


First, we substitute the values into the equation that we know.
$γ(R) = (5\cdot10^{12}) + (3/4\cdot1.39\cdot10^6)/R$. Simplified, this is:
$γ(R) = (5\cdot10^{12}) + (1.0425 \cdot 10^6)/R$


$γ(R)$ can be measured in your experiment. Then we can solve your equation for $R...$
$\large{R = \fbox{$\frac{1.0425 \cdot 10^6}{γ(R) - 5\cdot10^{12}}$}}$


Plug in your value of $γ(R)$, and you're there!\*



> 
> \*In other words, how should I use the λmax obtained through the experiment in the provided equation?
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> The equation only mentions $\gamma (R)$, I don't know how to help you there\*\*
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> 
> \*\*[Zhe](https://chemistry.stackexchange.com/users/35555/zhe): @JavaScriptCoder For these types of questions, the first thing to ask is "do you work in a lab?"
> If not, why are you doing experiments outside of a lab, and if so, why is it that no one in your lab has any expertise on this?
> 
> 
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