Given,
Stopping potential is V when the metal is illuminated with λ.
Stopping potential is 4V when the metal is illuminated with 2λ.
In photo electric effects
eV0=hν−W
eV0=λhc−W
eV=λhc−W ...(i)
e4V=2λhc−W ....(ii)
From (i) and (ii)
λhc−W=4(2λhc−W)
λhc−W=λ2hc−4W
3W=λhc⇒W=3λhc
λmaxhc=3λhc⇒λmax= threshold wavelength =3λ