The difference between threshold wavelengths for two metal surfaces...

The work function is given by

$\dfrac{hc}{\lambda} = ϕ$

$⇒ \lambda = \dfrac{hc}{ϕ}$

By the given data,

${\lambda}_{A} = \dfrac{1242}{9}nm$, ${\lambda}_{B} = \dfrac{1242}{4 . 5}nm$,

The difference between the wavelengths,

${\lambda}_{B} - {\lambda}_{A} = \dfrac{1242}{4 . 5} - \dfrac{1242}{9}nm = \dfrac{1242}{9}nm$

$= 138nm$