What is the threshold frequency of a photon to excite and then emit photoelectrons from a material?

Use the photoelectric effect equation which shows conservation of energy between photons, electrons and the material that the electron is being freed from, hf = phi + KE_max . Defining terms: h is Planck's constant, phi is the work function of the material (i.e. the energy needed to excite an electron from its surface) and KE_max is the maximum possible Kinetic Energy of the emitted photoelectron. Thus, to find the threshold frequency, i.e. the minimum frequency of light to cause photoelectric effect and excite an electron, set KE_max to zero (i.e. the condition of electron only just escaping, with no KE). Hence threshold frequency, f₀ = phi / h.