Photoelectric effect problem: How do you find threshold wavelength and extraction work?

The basic equation governing the photoelectric effect is -

Ep = WF + KE

where Ep = the energy of the photon = hc/λ, WF = the work function of the surface (extraction work), and KE = kinetic energy of the emitted electron = 0.5mv^2 (m = mass of electron, h = Planck's constant, c = speed of light))

we can write -

Case 1: hc/λ1 = WF + 0.5 m v1^2
Case 2: hc/λ2 = WF + 0.5*0.25 m v1^2

subtract to get hc(1/λ1 - 1/λ2) = m v1^2(0.5 - 0.125) = 0.375 m v1^2

If λ1and λ2 are known, this allows v1 to be calculated

WF (extraction work) can be calculated by substituting for v1 in the case 1 equation, and solving for WF.

The threshold wavelength is the wavelength which gives Ep = WF. When WF is known you can calculate the threshold wavelength λt by writing hc/λt = WF and solving for λt