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The constant A in the Richordson-Dushman...

The constant `A` in the Richordson-Dushman equation is `60 xx 10^4 A m^(-2) K^(-2)` for tungsten. A tungsten cathode has a total surface area of `2.0 xx 10^(-5) m^2` and operates at `2000 K`. The work function of tungsten is `4.55 eV`. Calculate the electric current due to thermionic emission.

Text Solution

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The Richardson-Dushman equation is
`I = AST^2 e^(-varphi)/(kT)`
We have, `varphi/kT = (4.55 eV)/((8.62 xx 10^(-5) eV K^(-1) (2000 K)`
`=26.4`.
Thus, the thus, the thermionic current `i` is
`=60 xx 10^4 A m^(-2) K^(-2) xx (2.0 xx 10^(-5) xx (2000 K)^2 xx e^(-26.4)`
`= (4.8 xx 10^5 A) e^(-264) = 0.16 mA`.
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