Q. 9

# The constant A in the Richardson-Dushman equation of tungsten is 60 × 10^{4} A m^{-2} K^{-2}. The work function surface area 2.0 × 10–5 m^{2} 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 × 10^{4} A m^{-2} K^{-2}

S=2.0 × 10–5 m^{2}

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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