An electron in an atom makes transitions between three energy levels E₃ , E₂ , and E₁ where E₃ > E₂ > E₁ . The wavelength of the photon emitted during the transition from E₃ to E₁ is 400 nm , and the wavelength of the photon emitted during the transition from E₂ to E₁ is 600 nm . The wavelength of the photon emitted during the transition from E₃ to E₂ is:

Step-by-step solution

Let the energy levels be E₃ , E₂ , and E₁ . The energy difference for a transition is related to the wavelength by E = hc . For the transition from E₃ to E₁ : E₃ - E₁ = hc ₃₁ = hc 400 For the transition from E₂ to E₁ : E₂ - E₁ = hc ₂₁ = hc 600 We need the wavelength ₃₂ for the transition from E₃ to E₂ , which corresponds to the energy difference: E₃ - E₂ = hc ₃₂ We can write the energy difference E₃ - E₂ as: E₃ - E₂ = (E₃ - E₁) - (E₂ - E₁) Substituting the expressions for energy differences: hc ₃₂ = hc 400 - hc 600