Question

An electron is trapped in a 1-dimensional box that is 576 nm wide. initially, it is in the n = 4 energy level, but after a photon is absorbed the electron is in the n = 5 energy level. what was the wavelength of the absorbed photon?

Answer 1

Energy of electron in atom level n = $\frac{-13.6 }{n^2} eV$

    When n = 4

          $E_4 = \frac{-13.6}{4^2} eV = -0.85 eV$

   When n = 5

          $E_5 = \frac{-13.6}{5^2} eV = -0.544 eV$

   Energy of photon absorbed = -0.544 - (-0.85) = 0.306 eV = 0.489 * $10^{-19}$ J

 We also have energy of photon = $\frac{hc}{\lambda } = \frac{1.99*10^{-25}}{\lambda}$

Comparing both    

    $0.489 * 10^{-19}= \frac{1.99*10^{-25}}{\lambda}\\ \\ \lambda = 4.069*10^{-6}m = 4069 nm$

So, Energy of photon = 4069 nm