Determine the wavelength of the line in the hydrogen atom spectrum corresponding to the n₁  2 to n₂  6 transition. A)1,275 nm B)1,034 nm C)595 nm D)410 nm E)225 nm

Question

Quizplus · Accepted Answer

The wavelength of the line in the hydrogen atom spectrum for a transition 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 ($ 1.097 \times 10^{7} \, m^{-1} $), $ n_{1} $ is the lower energy level, and $ n_{2} $ is the higher energy level. For the transition from $ n = 2 $ to $ n = 6 $, plugging in the values gives $ \frac{1}{\lambda} = 1.097 \times 10^{7} \left( \frac{1}{2^{2}} - \frac{1}{6^{2}} \right) $, which calculates to a wavelength $ \lambda $ close to 410 nm.

Determine the Wavelength of the Line in the Hydrogen Atom