 Radius of gyration of a uniform sphere

ID: radius-of-gyration-of-a-uniform-sphere

R

, the squared radius of gyration about its centre is the mass-weighted mean of

r^{2}

R_{g}^{2} = \frac{\int _{0}^{R} r ^{2} 4 π ρ r ^{2} d r}{4 π ρ R ^{3} /3} = \frac{3}{5} R^{2} .

Thus its volume is

(4 π /3) (5/3)^{3/2} R_{g}^{3}

, about

9.01 R_{g}^{3}

. A nonuniform object or a different shape need not obey this conversion. This distinction matters when estimating molecular number density from scattering measurements of a radius of gyration.

 New to topics? Read the docs here!