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When white light is scattered from a liquid a strong absorption line seen at 400nm and...

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When white light is scattered from a liquid a strong absorption line seen at 400nm and two emission lines are observed one of which is at 500nm and another in the infrared portion of the spectrum. What is the wave length of the second emission line.

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Let the wavelength of the second emitted light be X nm.

Applying Conservation of Energy for the absorption-emission phenomenon, it follows that:

` `E_(absorbed) = E_(emitted)  where,`E=(h*c)/lambda`

`rArr` (h*c)/`lambda` _absorbed=(h*c)/`lambda` _emitted(1) + (h*c)/`lambda` _emitted(2)

Cancelling (h*c) from both sides,

`rArr` 1/`lambda` _absorbed=1/`lambda` _emitted(1) + 1/`lambda`_emitted(2)

Putting the values,

`1/400=1/500+1/X`

`rArr X=2000 ` nm

Therefore, the wavelength of the second emitted line is 2000 nm. This falls in the infrared region of the electromagnetic spectrum.

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