We know that,
hν−ωo=12mv2max
=>hcλ=hcλo=12mv2max
=> hc(λo−λλλo)=12mv2max
vmax=√2hcm(λo−λλλo)---------- (1)
When wavelength is 3λ4 and velocity is v'
then v/=√2hcm[λo−(3λ/4)(3λ/4)×λo]−−−−−−−(2)
Dividing equation, (2) by (1),
v/v=√[λo−(3λ/4)](34)λλo×λλoλo−λv/=v(43)12√[λo−(3λ/4)]λo−λ
that is, v/=v(43)12