When the energy of the incident radiation is increased by 20%, the...

We know that, K{E}_\max = hv - ψ

Let initial frequency of the light be $ν$ and final frequency be $ν '$. According to question, final energy of light is $20$ more than initial energy.

$∴$$ν ' = 1 . 2ν$

In the 1st case,
$0.5eV = hv -$ ψ ...(i)

In the 2nd case,
$0.8eV = 1.2hv -$ ψ ...(ii)

Solving (i) and (ii) simultaneously, we get,

ψ $= 1eV$