When a metal surface is illuminated by light of wavelengths 400 nm and 250 nm, the maximum velocities of the photoelectrons ejected are v and 2v respectively. The work function of the metal is (h = Planck’s constant, c = velocity of light in air)
2 hc×106J
By using hcλ=W0+12mv2
⇒hc400×10−9=W0+12mv2 ⋯(i)
and hc250×10−9=W0+12m(2v)2 ⋯(ii)
On solving (i) and (ii)
12mv2=hc3[1250×10−9−1400×10−9] ⋯(iii)
From equation (i) and (iii) W0=2hc×106 J