This question is from the unit of Matter and Radiation.
According to the data given, the way to solve this is, using the einstein' s equation.
hf = Φ + K max
hc/λ = Φ + K max ----(1)[ As f = c/λ ]
When the wave length is λ, K max is 2eV.
hc/λ = Φ + 2 --------(2)
When the wave length is increased to 2λ, K max is 0.5 eV
hc/2λ = Φ + 0.5 --------(3)
From (2) to (3)
1/2(Φ + 2) = Φ + 0.5
Φ = 1 eV
hc/λ = 1 + 2
hc = 3λ
Let' s, the threshold wave length for photo electric emission from the surface as, λο
Φ = hfο
Φ = hc/λο
1 = 3λ/λο
λο = 3λ
The photo electric work function Φ = 1 eV
The threshold wave length for photo
electric emission from the surface. = 3λ