The wavelength of light in the visible region is about $390\; nm$ for violet colour,about $550\; nm$ (average wavelength) for yellow-green colour and about $760\; nm$ for red colour.
$(a)$ What are the energies of photons in $(eV)$ at the $(i)$ violet end,$(ii)$ average wavelength (yellow-green colour),and $(iii)$ red end of the visible spectrum? (Take $h=6.63 \times 10^{-34} \;J s$ and $1 \;eV = 1.6 \times 10^{-19} \;J$)
$(b)$ From which of the photosensitive materials with work functions listed in the table,and using the results of $(i), (ii)$ and $(iii)$ of $(a)$,can you build a photoelectric device that operates with visible light?

Metal	Work function $\phi_{0} (eV)$	Metal	Work function $\phi_{0} (eV)$
$Cs$	$2.14$	$Al$	$4.28$
$K$	$2.30$	$Hg$	$4.49$
$Na$	$2.75$	$Cu$	$4.65$
$Ca$	$3.20$	$Ag$	$4.70$
$Mo$	$4.17$	$N$	$5.15$
$Pb$	$4.25$	$Pt$	$5.65$

(N/A) The energy of an incident photon is given by $E = h\nu = hc / \lambda$.
Using $h = 6.63 \times 10^{-34} \; J s$ and $c = 3 \times 10^8 \; m/s$,we get $hc = 1.989 \times 10^{-25} \; J m$.
$(i)$ For violet light,$\lambda_1 = 390 \; nm = 390 \times 10^{-9} \; m$:
$E_1 = (1.989 \times 10^{-25}) / (390 \times 10^{-9}) \approx 5.10 \times 10^{-19} \; J = 3.19 \; eV$.
$(ii)$ For yellow-green light,$\lambda_2 = 550 \; nm = 550 \times 10^{-9} \; m$:
$E_2 = (1.989 \times 10^{-25}) / (550 \times 10^{-9}) \approx 3.62 \times 10^{-19} \; J = 2.26 \; eV$.
$(iii)$ For red light,$\lambda_3 = 760 \; nm = 760 \times 10^{-9} \; m$:
$E_3 = (1.989 \times 10^{-25}) / (760 \times 10^{-9}) \approx 2.62 \times 10^{-19} \; J = 1.64 \; eV$.
$(b)$ $A$ photoelectric device operates if the incident photon energy $E \geq \phi_0$.
For violet light $(3.19 \; eV)$,it can operate with $Cs$ $(2.14 \; eV)$,$K$ $(2.30 \; eV)$,and $Na$ $(2.75 \; eV)$.
For yellow-green light $(2.26 \; eV)$,it can operate with $Cs$ $(2.14 \; eV)$.
For red light $(1.64 \; eV)$,no material listed has a work function low enough to operate.