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Shane Macguire Grade: upto college level
        The constant A in the Richardson-Dushman equation for tungsten is 60 × 10^4 A/m^2-K. The work function of tungsten is 4.5 eV. A tungsten cathode having a surface area 2.0 × 10^-5 m^2 is heated by a 24 W electric heater. In steady state, the heat radiated by the cathode 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-K4. Assume that the thermions take only a small fraction of the heat supplied.
3 years ago

Answers : (1)

Aditi Chauhan
askIITians Faculty
396 Points
										Sol. A = 60 * 10^4 A/m^2 – k^2

∅ = 4.5 eV σ = 6 * 10^–8 ω/m^2 – k^4
S = 2 * 10^–5 m^2 K = 1.38 * 10^–23 J/K
H = 24 ω’
The Cathode acts as a black body, i.e. emissivity = 1
∴ E = σ A T^4 (A is area)
⇒ T^4 = E/σA = 24/6 * 10^-8 *2 * 10^-5 = 2 * 10^13K = 20 *10^12K
⇒ T = 2.1147 * 10^3 = 2114.7 K
Now, i = AST^2 e^-∅/KT
= 6 * 10^5 * 2 * 10^-5 * (2114.7)^2 * e^-4.5*1.6*10^-19/1.38*T*10^23
= 1.03456 * 10^-3 A = 1 mA
3 years ago
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