RICHARDSON’S APPARATUS | OMLABS | work function of diode

Описание: NOTE:
The T in K in calculated corresponding to the value of Rt/R273. A table is given for this in the instruction manual.
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To determine the work function of a diode or filament using Richardson's apparatus, you'll need to measure the thermionic emission current from the heated filament at different temperatures and then plot the data to extract the work function. The core concept relies on the Richardson-Dushman equation, which describes the relationship between thermionic current density and temperature.
Work Function of Diode and Richardsons Equation Kit India ...
Here's a more detailed breakdown:
1. Apparatus and Setup:
Vacuum Diode Tube:
A diode tube with a heated filament (cathode) and an anode (plate) placed in a vacuum.
Heater Circuit:
A DC power supply to heat the filament and control its temperature.
Measuring Instruments:
Ammeters to measure filament current, anode current, and possibly a voltmeter to measure filament voltage.
Temperature Measurement:
A way to determine the filament temperature, which can be done using the filament resistance and a known relationship between resistance and temperature.
2. Procedure:
1. Measure Filament Current and Anode Current:
Apply different heater currents to the filament and record the corresponding anode current (thermionic emission current) and filament current.
2. Calculate Filament Temperature:
Use the measured filament current and resistance (using Ohm's Law) to calculate the temperature of the filament.
3. Plot the Data:
Plot the log(anode current / T²) versus 1/T (where T is the filament temperature in Kelvin).
4. Analyze the Plot:
The plot should ideally be a straight line.
The slope of the line is directly related to the work function of the filament material.
3. Richardson-Dushman Equation:
The Richardson-Dushman equation relates the thermionic current density (J) to the temperature (T) and work function (φ):
J = AT² exp(-φ/kT)
Where:
J is the current density
A is the Richardson constant
T is the temperature in Kelvin
φ is the work function
k is the Boltzmann constant
By plotting log(J/T²) vs 1/T, you get a linear relationship, and the slope of this line allows you to calculate the work function.
4. Calculation of Work Function:
The slope (m) of the plot is related to the work function by the following formula:
m = -φ/k
Where:
φ is the work function
k is the Boltzmann constant (8.617 x 10^-5 eV/K)
Therefore, the work function can be calculated as:
φ = -k/m

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