Q. 7

A tungsten cathode and a thoriated-tungsten cathode have the same geometrical dimensions and are operated at the same temperature. The thoriated-tungsten cathode gives 5000 times more current than the other one. Find the operating temperature. Take relevant data from the previous problem.

Answer :

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.


Given,


Attungsten=3 × 104 A m-2 K-2


Aptungsten=60× 104 A m-2 K-2


Φttungsten =2.6 eV


Φptungsten =4.5 eV


Ittungsten=5000Iptungsten





Taking log on both sides,



K


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