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 (ii) red end of the visible spectrum ? (Take h = `6.63 xx 10^(-34)` J s and 1 eV= ` 1.6 xx 10^(-19)` J ) ,

Explanation

(a) Eneergy of the incident photon, `E=hv=hc//lambda`
`E=(6.63xx10^(-34)Js)(3xx10^(8)m//s)//lambda`
`=(1.989xx10^(-25)Jm)/(lambda)`
(i) For violet light, `lambda_(1)=390nm" (lower wavelength end)"`
`"Incident photon energy, "E_(1)=(1.989xx10^(-25)Jm)/(390xx10^(-9)m)`
`=5.10xx10^(-19)J`
`=(5.10xx10^(-19)J)/(1.6xx10^(-19)J//eV)`
`=3.19eV`
(ii) For yellow - green light, `lambda_(2)=550nm" (average wavelength)"`
`"Incident photon energy, "E_(2)=(1.989xx10^(-25)Jm)/(550xx10^(-9)m)`
`=3.62xx10^(-19)J=2.26ev`
(iii) For red light, `lambda_(3)=760nm" (higher wavelength end)"`
`"Incident photon energy, "E_(3)=(1.989xx10^(-25)Jm)/(760xx10^(-9)m)`
`=2.62xx10^(-19)J=1.64ev`
(b) For a photoelectric device to operate, we require incident light energy E to be equal to or greater than the work function `phi_(0)` of the material. Thus, the photoelectric device will operate with violet light (with E = 3.19 ev) photosensitive material `Na ("with "phi_(0) = 2.75 eV), K ("with "phi_(0) = 2.30 eV) and Cs ("with "phi_(0) = 2.14 eV)`. It will also operate with yellow-green light `("with E "= 2.26 eV)" for Cs "("with "phi_(0) = 2.14 eV)` only. However, it will not operate with red light (with E = 1.64 eV) for any of these photosensitive materials.