Suppose i₀ represents the thermionic current emitted from a metal surface at an absolute temperature T₀ . If the temperature is gradually increased and the thermionic current is recorded as a function of temperature, which of the following graphs could illustrate the variation of (i/i₀) with respect to (T/T₀) ?

Step-by-step solution

According to the Richardson-Dushman equation, the thermionic current i emitted from a metal surface at an absolute temperature T is given by: i = A T^2 e^ - W kT where A is a constant, W is the work function of the metal, and k is the Boltzmann constant. At temperature T₀ , the current is: i₀ = A T₀^2 e^ - W kT₀ Taking the ratio of the two currents, we get: i i₀ = ( T T₀ )^2 e^ W k ( 1 T₀ - 1 T ) Let y = i i₀ and x = T T₀ . The equation becomes: y = x^2 e^ W kT₀ (1 - 1 x ) As x (or T/T₀ ) increases, both the x^2 te