If there are 10 billion transistors (each of a square shape) uniformly (without space) distributed on a silicon chip with the squared area of 1 cm^2, what is the linear size of each unit?

the transistors have L=1 mm of linear size

Step-by-step explanation:

For the silicon chip the area is A=1 cm² and for the transistors the area is At=L² (L=linear size). Then since N = 10 billion transistors of area At should fit in the area A

A=N*At

A=N*L²

solving for L

L = √ (A/N)

Assuming that 1 billion=10⁹ (short scale version of billion), then

L = √ (A/N) = √ (1 cm²/10⁹) = 1 cm / 10³ = 1 mm

then the transistors have L=1 mm of linear size