The temperature variation of the work function of clean and of thoriated tungsten

It is well known that the relation between the electron emission i from a hot body and its absolute temperatureT may be expressed empirically by the equation i =AT 2 e -ψ/kT , in whichA and ψ are constants characteristic of the emitting surface, andk is Boltzmann’s constant. This is of the same form as the theoretical equation i =A0 D- T2 e -x/kT , in whichA 0 is a universal constant having the numerical value of 120 amp. cm.-2 degree-2 ,D - is the mean transmission coefficient, andX is the work function of the emitter. This quantity is not necessarily constant with temperature, and if we assume its temperature variation to be linear, as we may do within a sufficiently restricted range of temperatures, settingX = ω+αKT , Where ω and α are Constants, we may rewrite(2) thus: i =A0 D- T2 e -ω/kT . It may be shown (cf. Reimann 1934a, p. 265) that in such cases as occur in natureD - probably never varies appreciably with temperature, and so, assuming this, and comparing (1) with (4), we may writeA = A0 D- e-α, ψ = ψ.