The stopping potential V _ o (in volt) as a function of frequency (...

From Einstein's photoelectric equation, $hν = ϕ + e{V}_{0}$.

$⇒ {V}_{0} = \dfrac{hν}{e} - \dfrac{ϕ}{e} . . . . . . \left(1\right)$

At $ν = 4 \times {10}^{14}Hz$, ${V}_{0} = 0$.

Putting the value in equation \left(1\right)$, we get</p><p>$0 = \dfrac{hv}{e} - \dfrac{ϕ}{e}$</p><p>So, Work function$( ϕ ) = \dfrac{\left(hν\right)}{e}\left(ineV\right)$<br />$= \dfrac{6.63 \times {10}^{- 34} \times \left(4 \times {10}^{14}\right)}{1.6 \times {10}^{- 19}}$<br />$= 1.66eV