The wavelength of light in the visible region is about 390 nm for violet colour, about 550 nm (average wavelength) for yellowgreen 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 "= 6.63xx10^(-34)" J s and 1 eV" = 1.6xx10^(-19)J.)`
(b) From which of the photosensitive materials with work functions listed in Table 11.1 and using the results of (i), (ii) and (iii) of (a), can you build a photoelectric device that operates with visible light?

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.