Suppose i_0 represents the thermionic current emitted from a metal...

According to the Richardson-Dushman equation, the thermionic current $i$ emitted from a metal surface at an absolute temperature $T$ is given by:

$i = A T^2 e^{-\dfrac{W}{kT}}$

where $A$ is a constant, $W$ is the work function of the metal, and $k$ is the Boltzmann constant.

At temperature $T_0$, the current is:

$i_0 = A T_0^2 e^{-\dfrac{W}{kT_0}}$

Taking the ratio of the two currents, we get:

$\dfrac{i}{i_0} = \left(\dfrac{T}{T_0}\right)^2 e^{\dfrac{W}{k}\left(\dfrac{1}{T_0} - \dfrac{1}{T}\right)}$

Let $y = \dfrac{i}{i_0}$ and $x = \dfrac{T}{T_0}$. The equation becomes:

$y = x^2 e^{\dfrac{W}{kT_0}\left(1 - \dfrac{1}{x}\right)}$

As $x$ (or $T/T_0$) increases, both the $x^2$ term and the exponential term $e^{\dfrac{W}{kT_0}\left(1 - \dfrac{1}{x}\right)}$ increase. The function grows very rapidly, meaning its slope continuously increases (the curve is concave upwards).

Looking at the given graphs:
- Curve a has a negative slope.
- Curve b is a straight line (constant slope).
- Curve c is concave downwards.
- Curve d is concave upwards and shows rapid exponential growth.

Thus, curve d correctly illustrates the variation of $i/i_0$ with respect to $T/T_0$.