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Question

A gas absorbs a photon of 355 nm and emits it at two wavelengths. If one of the emissions is at 680 nm, what will be the next wavelength emitted?


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Solution

Conservation of Energy

  • According to the Law of conservation energy, the absorbed photon must be equal to the combined energy of the emitted photons
    EA=E1+E2+
    Here, EA is the energy of the absorbed photon.
    E1andE2are the energy of the emitted photons.

Calculation of the second wavelength

  • Step 1: Relationship between energy and the wavelength
    E=hcλ
    Here, E represents energy
    h represents Planck's constant
    c represents velocity
    λ represents wavelength
  • Step 2: Determination of the second wavelength
    The wavelength of the absorbed photon (λA) = 355 nm
    The wavelength of the emitted photon (λ1) = 680 nm
    hcλA=hcλ1+hcλ21λA=1λ1+1λ21355=1680+1λ21λ2=1355-1680λ2=743nm

Therefore, the wavelength of the second emitted photon is 743 nm.


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