The number of thermions emitted in a given time increases 100 times as the temperature of the emitting surface is increased from `600 K to 800 K`. Find the work function of the emitter. Boltzmann constant `k = 8.62 xx 10^(-5) eV k^(-1)`.

Explanation

The number of thermions `n,` emitted by a surface, in a given time is given by (Richardson-Dushman equation)
`n = A'ST^2 e^(-varphi/(kT)`
where `A'` is a constant and other symbols have their usual meanings. Let `n_1 and n_2` be the number of electrons emitted at temperatures `T_1 and T_2`. Then
`n_1/n_2 = T_1^2/T_2^2 (e^(-varphi/(kT_1)/(e^(-varphi)/(kT_2)`
or, `(n_1 T_2^2)/(n_2 T_1^2) = e^(- (varphi)/k (1/T_1 - 1/T_2)`
or, `- (varphi/k) (1/T_1 - 1/T_2) = 1n (n_1/T_2^2)/(n_2 T_1^2)`
`or, (varphi(T_2 - T_1))/(kT_1 T_2) = 1n (n_2 T_1^2)/(n_1 T_2^2)`
or, `varphi = (kT_1 T_2)/(T_2 - T_1) 1n (n_2 T_1^2)/(n_1 T_2^2)`
`= ((8.62 xx 10^(-5) eV K^(-1) (600 K) (800 K))/(200 K) 1n (100 xx 36/64)`
`0.83 eV`.