?Evaluate the radius of gyration, \(R_{\mathrm{g}}\), of (a) a solid sphere of radius

Chapter 14, Problem P14D.1

(choose chapter or problem)

Evaluate the radius of gyration, \(R_{\mathrm{g}}\), of

(a) a solid sphere of radius a,

(b) a long straight rod of radius a and length l. Show that in the case of a solid sphere of specific volume \(v_{s}\), \(R_{\mathrm{g}} / \mathrm{nm} \approx 0.056902 \times\left\{\left(v_{\mathrm{s}} / \mathrm{cm}^{3} \mathrm{~g}^{-1}\right)\left(M / \mathrm{g} \mathrm{mol}^{-1}\right)\right\}^{1 / 3}\).

Evaluate \(R_{\mathrm{g}}\) for a species with \(M=100 \mathrm{~kg} \mathrm{~mol}^{-1}\), \(v_{\mathrm{s}}=0.750 \mathrm{~cm}^{3} \mathrm{~g}^{-1}\), and, in the case of the rod, of radius 0.50 nm.

Text Transcription:

R_g

v_s

R_g nm approx 0.056902 times{(v_s/cm^3 g^-1)(M/g mol^-1)}^1/3

M=100 kg mol^-1

v_s=0.750 cm^3 g^-1