The ratio of thermionic currents (I/I_0) for | vedclass

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(A) According to Richardson-Dushman equation,the thermionic current $I$ is given by $I = AT^2 e^{-\phi/kT}$,where $A$ is a constant,$T$ is the absolut

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$A$

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(A) According to Richardson-Dushman equation,the thermionic current $I$ is given by $I = AT^2 e^{-\phi/kT}$,where $A$ is a constant,$T$ is the absolute temperature,$\phi$ is the work function,and $k$ is the Boltzmann constant.For a small range of temperature variation,the exponential term $e^{-\phi/kT}$ remains approximately constant.Therefore,the current $I$ is proportional to the square of the temperature: $I \propto T^2$.This implies the ratio $\frac{I}{I_0} = \left( \frac{T}{T_0} \right)^2$.This equation represents a parabola opening upwards,which corresponds to curve $A$ in the given figure.

The ratio of thermionic currents $(I/I_0)$ for a metal when the temperature is slowly increased from $T_0$ to $T$ is shown in the figure. ($I$ and $I_0$ are currents at $T$ and $T_0$ respectively). Which curve correctly represents this relationship?

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