Answer
$\phi_{0}^1\lt \phi_{0}^2\lt \phi_{0}^3$
Work Step by Step
We can find the work function $\phi$ from the cutoff frequency
$f_{0}$ using following relation:
$\phi=hf_{0}$
where $h$ is the Planck's constant
According to the figure 38-20, the order of cutoff wavelength is
$\lambda_{0}^1\gt \lambda_{0}^2\gt \lambda_{0}^3$
or, $\frac{1}{f_{0}^1}\gt \frac{1}{f_{0}^2}\gt \frac{1}{f_{0}^3}$
or, $f_{0}^1\lt f_{0}^2\lt f_{0}^3$
or, $\phi_{0}^1\lt \phi_{0}^2\lt \phi_{0}^3$
where, $\lambda_{0}^1$, $f_{0}^1$ and $\phi_{0}^1$ are the cutoff wavelength, cutoff frequency and work function of graph 1,
$\lambda_{0}^2$, $f_{0}^2$ and $\phi_{0}^2$ are the cutoff wavelength, cutoff frequency and work function of graph 2,
and $\lambda_{0}^3$, $f_{0}^3$ and $\phi_{0}^3$ are the cutoff wavelength, cutoff frequency and work function of graph 3.
Thus the rank of the materials according to their work function is $\phi_{0}^1\lt \phi_{0}^2\lt \phi_{0}^3$
