Answer
a) $1.6 \times 10^{-9} m$
b) $s = 5 \times 10^5$
Work Step by Step
The size is given by:
$S = A/N$
Where A is the area and N is the number of chips.
$S = \frac{(4 mm)^2}{10^{10}}$
$1.6 \times 10^{-9} mm^2$
b) We now find:
$t = \frac{Nd}{v}$
The speed is 2/3 the speed of light, so the number of calculations per second, s, is:
$s = 1/t = (\frac{10^{10}4*10^{-8}}{2/3*3*10^8})^{-1}$
$s = 5 \times 10^5$