Question

A rectangular cathode with the dimensions width = 3.5 mm and length = 37 mm glows at a temperature of 1800K in a vacuum tube. The work functionof the cathode is & = 2.5 eV and the emission constant is 3E4 Am-2K-2. What is the maximum (saturation) current that can be extracted from thiscathode?Hint: If you use the Boltzmann constant in eV enter at least 5 significant digits (i.e. use 8.6174E-5 eV K-1)

Answer 1

16.12 A

Step-by-step explanation:

The maximum (saturation) current that can be extracted from the cathode can be calculated using the Richardson-Dushman equation. The equation is given by:

Js = AT^2exp(-W/kT)

where Js is the saturation current density, A is the emission constant, T is the temperature of the cathode in Kelvin, W is the work function of the cathode in eV, k is the Boltzmann constant in eV/K.

Substituting the given values into the equation we get:

Js = 3E4 * 1800^2 * exp(-2.5 / (8.617333262145E-5 * 1800))

Js = 1.246E8 A/m^2

The area of the cathode is given by width * length = 3.5E-3 * 37E-3 = 0.0001295 m^2.

Therefore, the maximum (saturation) current that can be extracted from this cathode is given by Js * Area = 1.246E8 * 0.0001295 = 16.12 A. So, the maximum current that can be extracted from this cathode is 16.12 A.