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Question

A dye emits 50% of the absorbed energy as fluorescence. If the number of quanta absorbed and the emitted out are in ratio 1:4. Find the wavelength of emitted radiation if the absorbed radiation has a wavelength of x oA.

A
x oA
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B
0.5x oA
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C
4x oA
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D
8x oA
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Solution

The correct option is D 8x oA
We know, E = nhv = nhcλ where n is the number of photon absorbed or emitted
λ is the wavelength.
Given: Eemitted=50100×Eabsorbed

or, n1×hcλ1=12×n2×hcλ2
where n1 and n2 is the number of photons emitted and absorbed. And n1:n2 = 4 : 1
λ1λ2=21×n1n2=21×41

λ1x oA=81

λ1=8x oA

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