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.
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 x 10^–34 Js and 1 eV = 1.6 x 10^–19J).

Solution

Given,
Wavelength of violet colour,

λ_{v}

= 390 nm
Wavelength of yellow-green colour,

λ_{yg}

= 550 nm
Wavelength of red color,

λ_{r}

λ_{r}

= 760 nm

Energy of the incident photon,

E = hv = \frac{hc}{λ}

\Rightarrow

E = (6.63 \times 10^{- 34} Js) (3 \times 10^{8} {ms}^{- 1}) / λ

= \frac{1.989 \times 10^{- 25} Jm}{λ}

(i) For violet light,

λ_{1} = 390 nm (lower wavelength end)

Incident photon energy,

E_{1} = \frac{1.989 \times 10^{- 25} Jm}{390 \times 10^{- 9} m} = 5.10 \times 10^{- 19} J = \frac{5.10 \times 10^{- 19} J}{1.6 \times 10^{- 19} J / eV} = 3.19 eV

(ii) For yellow-green light, λ₂ = 550 nm (average wavelength)

Incident photon energy,

E_{2} = \frac{1.989 \times 10^{- 25} Jm}{550 \times 10^{- 9} m}

\Rightarrow

E_{2} = 3.62 \times 10^{- 19} J = 2.26 eV

(iii) For red light,

λ_{3} = 760 nm (higher wavelength end)

Incident photon energy,

E_{3} = \frac{1.989 \times 10^{- 25} Jm}{760 \times 10^{- 9} m}

\Rightarrow

E_{3} = 2.62 \times 10^{- 19} J = 1.64 eV .

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