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,

A_{ttungsten}=3 × 10^{4} A m-^{2} K^{-2}

A_{ptungsten=}60× 10^{4} 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

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