Question

You are an intern at Beckman Coulter. You oversee the design of instrumentation for a Coulter counter. In the device, a 72.6μm long and 22.2μm diameter tube filled with 0.2MKCl(rho=0.5Ω-m) is used as the channel. Determine the impedance of the channel without the presence of cells/particles. Your answer should be in kΩ.

Answer 1

The impedance of the channel in a Coulter counter can be found using the formula for the resistance of a cylindrical conductor. When calculated with the given dimensions and resistivity of the KCl solution, the result in ohms can then be converted to kilohms (kΩ) for the final answer.

Step-by-step explanation:

To determine the impedance of the channel without the presence of cells/particles in a Coulter counter, we will employ the formula for the resistance (or impedance since we're dealing with an electrolyte solution) of a cylindrical object:

R = ρL / A

where ρ is the resistivity of the solution, L is the length of the channel, and A is the cross-sectional area of the channel.

We're given: ρ = 0.5 Ω-m, L = 72.6µm, and diameter d = 22.2µm. To find the area A, we use the formula for the area of a circle:

A = πr²

where r is the radius of the channel.

First, convert the diameter to radius by dividing by 2, so r = 22.2µm / 2 = 11.1µm and convert it to meters: r = 11.1 x 10⁻¶m. Then, calculate the cross-sectional area:

A = π(11.1 x 10⁻¶m)²

Now, calculate the resistance (impedance) using the above values:

R = (0.5 Ω-m)(72.6 x 10⁻¶m) / π(11.1 x 10⁻¶m)²

Solving this will yield the impedance in ohms, which can then be converted to kilohms (kΩ) by dividing by 1000.