Question

As computer processor speeds increase, it is necessary for engineers to increase the number of circuit elements packed into a given area. Individual circuit elements are often connected using very small copper "wires" deposited directly onto the surface of the chip. In some processors, these copper interconnects are about wide. What mass of copper would be in a length of such an interconnect, assuming a square cross section? The density of copper is 8.96 g/cm^3.

Answer 1

Step-by-step explanation:

As the cross-section of wire is a square so, it means that height of the wire is same length as the width.

Now, we will convert both height and width into centimeters as follows.

h = w

=
`(22 nm * 10^(-9) m)/(1 nm) * (1 cm)/(1 m)`

=
`2.2 * 10^(-6) cm`

Length of wire will also be converted into centimeters as follows.

l =
`(1 mm * 1 m)/(1000 mm) * (100 cm)/(1 m)`

= 0.1 cm

Now, we will calculate the volume of the wire as follows.

V =
`l * b * h`

=
`0.1 cm * 2.2 * 10^(-6) cm * 2.2 * 10^(-6) cm`

=
`4.84 * 10^(-13) cm^(3)`

Now, we will convert moles of copper into atoms of copper as follows.

`(4.84 * 10^(-13) cm^(3) * 8.96 g Cu * 1 mol Cu * 6.022 * 10^(23))/(1 cm^(3) Cu * 63.546 g Cu * 1 mol Cu)`

=
`4 * 10^(10) atom Cu`

Thus, we can conclude that there will be
`4 * 10^(10) \text{atom Cu}` would be in a length of such an interconnect, assuming a square cross section.