Final answer:
The volume of material for a single bit on a hard disk with a storage density of 100 gigabits per square inch and layer thickness of 20nm is calculated as a product of the area occupied by one bit and the layer thickness, resulting in a very small volume in cubic inches.
Step-by-step explanation:
To calculate the volume of material corresponding to a single bit on a modern magnetic hard disk with a storage density of 100 gigabits per square inch, first convert the density to cubic inches, accounting for the 20nm layer thickness. One square inch can hold 100 gigabits, so one bit occupies 1/100,000,000,000 of a square inch.
Converting the thickness to inches (20 nm is 20 x 10-9 meters, and there are 39.3701 inches in a meter), we get 20 x 10-9 x 39.3701 = 7.87402 x 10-7 inches. Therefore, the volume of material for a single bit is (1/100,000,000,000) square inches times 7.87402 x 10-7 inches, giving a tiny volume of 7.87402 x 10-7 / 100,000,000,000 cubic inches.