Page 40 - Science at the nanoscale

7:14
RPS: PSP0007 - Science-at-Nanoscale
June 9, 2009
ch02
30
Classical Physics at the Nanoscale
3. Calculate the Brownian diffusion length for a spherical
nanobot of radius 200 nm inside the bloodstream of a living
human being. Describe its motion inside the bloodstream,
assuming the nanobot has no internal propulsion motor. Note
that blood velocity can be as high as 1 m/s in the aorta and <1
mm/s in the capillaries.
4. Show that for a thin rod made of a material with Young’s mod-
ulus Y, density ρ, spring constant k, atomic spacing a and
atomic mass m:
2
Y
ka
(2.19)
=
m
ρ
Hint: The connection between the macroscopic and nano-
scopic quantities can be made by considering a linear chain
of N masses m separated by springs with spring constant k
and length a.