Calculate the wavelength of light emitted when an electron in the hydrogen atom goes from the n = 4 shell to the n = 2 shell.

Question

Quizplus · Accepted Answer

The wavelength of light emitted during a transition of an electron in a hydrogen atom can be calculated using the Rydberg formula: $ \frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) $, where $ \lambda $ is the wavelength, $ R $ is the Rydberg constant (approximately $ 1.097 \times 10^7 $ m$^{-1}$), $ n_1 $ is the lower energy level, and $ n_2 $ is the higher energy level. For a transition from $ n = 4 $ to $ n = 2 $, the calculation yields a wavelength in the range of the answer in option B, which is approximately $ 4.86 \times 10^{-7} $ meters or 486 nm, typical for the Balmer series of hydrogen.

Calculate the Wavelength of Light Emitted When an Electron in the Hydrogen