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.

Question

Philoid · Accepted 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,

A_ttungsten=3 × 10⁴ A m-² K^-2

A_ptungsten=60× 10⁴ A m-² K^-2

Φ_ttungsten =2.6 eV

Φ_ptungsten =4.5 eV

I_ttungsten=5000I_ptungsten

Taking log on both sides,

K