We know that, the photoelectric effect equation,
KE=hf−φ Here,
KE= kinetic energy of the electrons
h= Planck's constant
f= frequency of the light and
φ= work-function of the photocathodes.
For two identical photocathodes,
mv12=hf1−φ....(i)
mv22=hf2−φ.....(ii)
Since, the material of photocathodes is same, so the value of the work-function
φ is same.
Subtracting Eq. (ii) from Eq. (i) we get
mv12−mv22=hf1−hf2 v12−v22=(f1−f2)