Question

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 ) ,

Answer 1

Energy of the incident photon,
`E= hv = hc//lambda`
` E = (6.63 xx10^(-34) Js) (3 xx 10^(8) m//s)//lambda`
` = ((1.989xx10^(-25))Jm)/lambda `
(i) For violet light ,
`lambda _(1) = 390 ` nm (lower wavelength end)
Incident photon energy ,
` E_(1) = (1.989 xx 10^(-25)Jm)/(390xx10^(-9)m)`
` = 5.10xx10^(-19) J = (5.10xx10^(-19)J)/(1.6 xx 10^(-19)J//eV)`
= 3.19 eV
(ii) For yellow - green light ,
`lambda_(2) = 550 ` nm (average wavelength )
Incident photon energy ,
` E_(2) = (1.989 xx 10^(-25)Jm)/(550 xx10^(-9)m)`
` = 3.62 xx 10^(-19) J = 2.26 eV`
(iii) For red light ,
` lambda _(3) = 760` nm( higher wavelength end)
Incident photon energy
` E_(3) = (1.989 xx 10^(-25)Jm)/(760 xx 10^(-9) m)`
` = 2.62 xx 10^(-19) J = 1.64 eV`