Line spectra from all regions of the electromagnetic spectrum, including the Paschen series of infrared lines for hydrogen, are used by astronomers to identify elements present in the atmospheres of stars. Calculate the wavelength of the photon emitted when the hydrogen atom undergoes a transition from n = 5 to n = 3. (R = 1.096776 × 10⁷ m^-1) A) 205.1 nm B) 384.6 nm C) 683.8 nm D) 1282 nm E) 1500 nm

Question

Line spectra from all regions of the electromagnetic spectrum, including the Paschen series of infrared lines for hydrogen, are used by astronomers to identify elements present in the atmospheres of stars. Calculate the wavelength of the photon emitted when the hydrogen atom undergoes a transition from n = 5 to n = 3. (R = 1.096776 × 10⁷ m^-1) A) 205.1 nm B) 384.6 nm C) 683.8 nm D) 1282 nm E) > 1500 nm

Quizplus · Accepted Answer

The wavelength of the photon emitted during the transition from n = 5 to n = 3 in hydrogen can be calculated using the Rydberg formula for hydrogen: 1/λ = R * (1/n1² - 1/n2²). Substituting n1 = 3, n2 = 5, and R = 1.096776 × 10⁷ m⁻¹, we find λ ≈ 1282 nm.

Line Spectra from All Regions of the Electromagnetic Spectrum, Including