If p is the momentum of the fastest electron ejected from a metal...

$hν - ϕ = KE$

${\left(\dfrac{hc}{\lambda}\right)}_{incident} = KE + ϕ$

Given \left(ϕ < < KE\right)$</p><p>${\left(\dfrac{hc}{\lambda}\right)}_{incident} \approx KE$</p><p>${\left(\dfrac{hc}{\lambda}\right)}_{incident} = \dfrac{{p}^{2}}{2m}$......(i)</p><p>\left(\dfrac{hc}{\lambda '}\right) = \dfrac{{\left(1.5p\right)}^{2}}{2m}$ …….(ii)

Divide (i) and (ii)

$\dfrac{{\lambda}^{'}}{\lambda} = \dfrac{{p}^{2}}{2.25{p}^{2}}$

${\lambda}^{'} = \dfrac{\lambda \times 100}{2.25} = \dfrac{4}{9}$

${\lambda}^{'} = \dfrac{4}{9}\lambda$