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Question

A dye absorbs a photon of wavelength λ and re-emits the same energy into two photons of wavelength λ1 and λ2 respectively. The wavelength λ is related to λ1 and λ2 as?


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Solution

Step 1: Given

Assume E to be the energy of photon of wavelength λ

Assume E1 to be the energy of photon of wavelength λ1

Assume E2 to be the energy of photon of wavelength λ2

Step 2: Formula Used

Energy of a photon is given as E=hcλ, where h is Planck's constant and c is speed of light.

Step 3: Solution

The energy of the photon of wavelength λ will be equal to the sum of energies of the photons with wavelengths λ1 and λ2, because they are re-emitted from that photon. Thus,

E=E1+E2hcλ=hcλ1+hcλ2hcλ=hc1λ1+1λ21λ=1λ1+1λ21λ=λ1+λ2λ1λ2λ=λ1λ2λ1+λ2

Hence, the relation is λ=λ1λ2λ1+λ2.


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