A light beam with wavelengths distributed uniformly between 450 nm and 550 nm is passed through a sample of hydrogen gas. Which wavelength will exhibit the least intensity in the transmitted beam?

Step-by-step solution

The least intensity in the transmitted beam corresponds to the wavelength that is absorbed by the hydrogen gas. The given wavelength range is 450 nm to 550 nm , which falls in the visible region. Absorption in the visible region corresponds to the Balmer series, where the electron transitions from the n = 2 state to a higher energy level. The energy of an electron in the n^ th orbit of a hydrogen atom is given by: E_n = - 13.6 n^2 eV For the n = 2 state, E₂ = -3.4 eV . For the n = 3 state, E₃ = -1.51 eV . The energ