Q. 9

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.

Answer :

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





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