If the threshold wavelength for sodium is `5420 Å`, then the work function of sodium is

Explanation

KEY IDEAS
We can find the work function `Phi` from the cutoff frequency `f_(0)` (which we can measure on the plot). The reasoning is this : At the cutoff frequency, the kinetic energy `K_("max")` in Eq. 37-5 is zero. Thus, all the energy hf that is transferred from a photon to an electron goes into the electron.s escape, which requries an energy of `Phi`.
Calculations : From that last idea, Eq. 37 - 5 then gives us, with `f=f_(0)`,
`hf_(0)=0+Phi=Phi`
In the cutoff frequency `f_(0)` is the frequency at which the plotted intercepts the horizontal frequency axis, about `5.5xx106(14)Hz`. We then have
`Phi=hf_(0)=(6.63xx10^(-34)J.s)(5.5xx10^(14)Hz)`
`=3.6xx10^(-19)J=2.3eV.`