Question

Estimate the surface-to-volume ratio of a C60 fullerene by treating the molecule as a hollow sphere and using 77pm for the atomic radius of carbon.

Answer 1

Answer:

The surface-to-volume ratio of a C-60 fullerene is 3:77.

Explanation:

Surface area of sphere = $S=4\pi r^2$

Volume of the sphere = $V=\frac{4}{3}\pi r^3$

where : r  = radius of the sphere

Radius of the C-60 fullerene sphere = r = 77 pm

Surface area of the C-60 fullerene = $S=4\pi (77 pm)^2$...[1]

Volume area of the C-60 fullerene = $V=\frac{4}{3}\pi (77 pm)^3$..[2]

Dividing [1] by [2]:

$\frac{S}{V}=\frac{4\pi (77 pm)^2}{\frac{4}{3}\pi (77 pm)^3}$

$=\frac{3}{77}$

The surface-to-volume ratio of a C-60 fullerene is 3:77.