When light has exactly the same energy as the work done function of a metal surface then:

Explanation

no photoelectric current is produced although photoelectrons are emitted they do not move or do not have kinetic energy as, hv = W ( work function = hv0) +Ek where Ek =0 and v=v0 The work function of a metal is the energy corresponding to the threshold frequency of the metal. Albert Einstein used the work function of a metal to describe the photoelectric effect. The maximum kinetic energy of the ejected electrons depended on the frequency of the incident photon and the work function. K.E.max= hf - φ. The work function of metal can be interpreted as the minimum bond energy or the bond energy of the surface electrons. If the energy of the incident photons is equal to the work function, the kinetic energy of the released electrons will be zero and no photoelectric current will be observed. The electron is trapped inside a potential well which is created by the effect of the nucleus and other electrons. The work function is the energy required for the electron to reach to the top of the well. So, rationally thinking, a photon of energy equal to the work function will excite the electron to the top of the well and then the electron will get de-excited back to the bottom; thereby preventing the ejection and "f" energy of incident photon equals to work function then the ejected photon will have zero kinetic energy because the incident energy of electron will just act as ionizing energy. In this, we can also observe that photoelectrons are initially produced and a photoelectric effect is observed but t is compensated hence no current can be observed.