Question

Using the particle-in-the-box model for the hydrogen atom and treating the atom as an electron in a one-dimensional box of length 150. pm, predict the wavelength of radiation emitted when the electron falls from the level with n 3 to that with n 2

Answer 1

The model has resulted into a formula called the Rydberg formula. It also came about from the electron transfer within the hydrogen atom. The formula is shown in the picture, where RH is the Rydberg constant and λ is the wavelength . Thus, the solution is as follows:

1/λ = (1.0973731×10⁷ m⁻¹)(1/2² - 1/3²)
Solving for λ,
λ = 6.56×10⁻⁷ m