A certain gas absorbs photon of wavelength 4.0 10⁻⁷ ~m and emits radiation at two wavelengths. If one of the emissions occurs at 7.5 10⁻⁷ ~m , what is the wavelength at which the second emission occurs?

Step-by-step solution

The energy of the absorbed photon is given by E_ abs = hc _ abs . The energy of the emitted photons are E₁ = hc ₁ and E₂ = hc ₂ . According to the principle of conservation of energy, the energy absorbed must equal the sum of the energies emitted in the two-step process: E_ abs = E₁ + E₂ . Substituting the expressions for energy: hc _ abs = hc ₁ + hc ₂ . Dividing by hc : 1 _ abs = 1 ₁ + 1 ₂ . Given _ abs = 4.0 10⁻⁷ m = 400 nm and ₁ = 7.5 10⁻⁷ m = 750 nm . 1 400 = 1 750 + 1 ₂ . 1 ₂ = 1 400 - 1 750 = 750 - 400 400 75