The constant A in the Richardson-Dushman equation of tungsten is 60 × 104 A m-2 K-2. The work function surface area 2.0 × 10–5 m2 is heated by a 24 W electric equals the energy input by the heater and the temperature becomes constant. Assuming that the cathode radiates like a blackbody, calculate the saturation current due to thermions. Take Stefan constant =6 × 10-8 W m-2 K-4. Assume that the thermions take only a small fraction of the heat supplied.
Given
A=60 × 104 A m-2 K-2
S=2.0 × 10–5 m2
P=24 W
=6 × 10-8 W m-2 K-4
The power radiated by Stefen’s law is given by
According to Richardson-Dushman Equation thermionic current i is
where, n is the thermions emitted, S is the surface area, T is the absolute temperature, k is the Boltzmann constant, A is the constant depend on nature of metal and ϕ is the work function
