Chapter 1, Problem 1.24P

Catalytic converters use nanoscale particles of precious metals such as platinum to change pollutants in carexhaust into less harmful gases. Calculate the following quantities for a spherical particle of platinum with a diameter of 5.0 nm.
(a) Surface area in units of $\mu {\text{m}}^2\left(SA=4\pi r^2\right)$
(b) Volume in units of $\mu {\text{m}}^3\left(V=\frac{4}{3}\pi r^3\right)$
(c)Surface area to volume ratio in units of $\mu {\text{m}}^{-1}$
(d)A $5.0\mu \text{m}$ diameterparticle has a surface area to volume ratioof $0.6\mu {\text{m}}^{-1}$ . How many times larger is the surface area to volume ratio of the 5.0 nm particle than the $5.0\mu \text{m}$ particle?