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.

Question

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.

Philoid · Accepted 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