= Nanoparticle
A <nanoparticle> is a particle whose external dimensions lie on the <nanoscale>. Its behaviour can depend strongly on its size, shape and <surface chemistry>, even when its overall chemical <chemical composition> is fixed.
For a <sphere> of radius $r$, the ratio of <surface area> to <volume> is
$$
\frac{A}{V}=\frac{4\pi r^2}{(4/3)\pi r^3}=\frac{3}{r}.
$$
Halving $r$ therefore doubles the <surface area> exposed per unit <volume>. At fixed total <volume>, making many smaller particles exposes more material to the surrounding medium. This helps explain why <surface> reactions and attached molecules can have a large effect on <nanoparticles>.<What Is So Special about Nano? by the National Nanotechnology Coordination Office>[Scale at which surface behavior plays a larger role; sphere calculation derived here]{ref}
The size of an individual <nanoparticle> also differs from the size of an <particle aggregate> containing many particles. Reports of particle size consequently need to identify what was measured. <Gold nanoparticles> provide a visible example: their interaction with <light> can differ markedly from bulk <gold>.
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