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.

Explanation

Since ` i=ne or n=i/e `
'e' is same in all cases.
` We know, i= AST^2 e^(-phi/RT),`
` phi = 4.52 e.V, `
` K = 1.38 xx (10^-23)J/K.`
` n(1000) = As xx (1000)^2 `
` x e^(-4.52 xx 1.6 xx (10^-19)//1.38 xx (10^-23) xx 1000)`
` = (10^6) xx 1.7396 xx (10^-23) `
` = 1.7396 xx (10^-17)`
` T = 300K ` .
(a) `n(T)/n(100K) =`
`((As xx (300^2) xx e^(-4.52 xx 1.6 xx (10^-19)//1.38 xx (10^-23) xx 1000))/ (As xx 1.7396 xx (10^-17)))`
` = 1.340 xx (10^16) ` .