(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]N_{nano}=\left[1-\frac{3}{4}\left(\frac{r}{R}\right)+\frac{1}{16}\left(\frac{r}{R}\right)^3\right]N_{bulk}[/tex]

Solve for R.

2. Relevant equations

Algebra, come to bite me in the butt...

3. The attempt at a solution

[tex]\frac{N_{nano}}{N_{bulk}}=1-\frac{3}{4}\left(\frac{r}{R}\right)+\frac{1}{16}\left(\frac{r}{R}\right)^3[/tex]

[tex]\frac{N_{nano}}{N_{bulk}}-1=-\frac{12}{16}\left(\frac{r}{R}\right)+\frac{1}{16}\left(\frac{r}{R}\right)^3[/tex]

[tex]16\left[\frac{N_{nano}}{N_{bulk}}-1\right]=\frac{r^3}{R^3}-12\left(\frac{r}{R}\right)[/tex]

And I'm stuck...

Properly, this isn't a homework question at all; I'm trying to analyze experimental data and I'd rather not call my prof with an algebra question

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# Homework Help: Nanoparticle Algebra

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