Question

An experimenter wants to make a layer of carbon 70.0 Angstroms thick by evaporating carbon onto a clean glass surface in vacuum. (1Angstrom=10−10m .) He first lays down by evaporation a fairly thick layer, with a central strip masked so that it remains bare (the shaded semicircles shown below). Then, using another mask in the manner of a stencil, he evaporates onto the glass a strip of the same width running across he gap (the shaded vertical rectangle), meanwhile using the heavy patches as terminals for measurement of resistance. At what value of the resistance should he stop the evaporation? (The resistivity of carbon at room temperature is 3.50×10−5 Ωm .)

Answer 1

To find the resistance, we need to determine the resistance of the carbon layer with a thickness of 70.0 Angstroms.

First, we need to calculate the resistance R using the formula:

R = ρ * L / A

Where:
- ρ is the resistivity of carbon (given as 3.50 × 10^-5 Ω·m)
- L is the length of the carbon layer (which is the same as the width of the shaded vertical rectangle)
- A is the cross-sectional area of the carbon layer (which is the thickness multiplied by the width)

Given:
- Thickness of carbon layer: 70.0 Angstroms = 70.0 × 10^-10 m
- Resistivity of carbon: ρ = 3.50 × 10^-5 Ω·m
- Width of the shaded vertical rectangle: Not provided, but assumed to be known or can be measured.

Once we have the width of the shaded vertical rectangle, we can plug in the values and calculate the resistance R.