The wavelength of light emitted during a transition in the hydrogen atom can be calculated using the Rydberg formula:
1/λ = R * (1/n1^2 - 1/n2^2)
where λ is the wavelength of light, R is the Rydberg constant (approximately 1.097 × 10^7 m^-1), and n1 and n2 are the principal quantum numbers of the initial and final energy levels, respectively.
Let's calculate the wavelengths and identify the type of electromagnetic radiation emitted during the two transitions you mentioned:
- Transition from n = 3 to n = 2: For n1 = 3 and n2 = 2, the wavelength can be calculated as follows:
1/λ = R * (1/2^2 - 1/3^2) 1/λ = R * (1/4 - 1/9) 1/λ = R * (9/36 - 4/36) 1/λ = R * (5/36) λ = 36/(5 * R)
Calculating the value, we find: λ = 36 / (5 * 1.097 × 10^7) λ ≈ 6.563 × 10^-8 meters or 65.63 nm
The transition from n = 3 to n = 2 in the hydrogen atom emits light in the visible range. It falls within the red region of the spectrum.
- Transition from n = 2 to n = 1: For n1 = 2 and n2 = 1, the wavelength can be calculated similarly:
1/λ = R * (1/1^2 - 1/2^2) 1/λ = R * (1/1 - 1/4) 1/λ = R * (3/4) λ = 4 / (3 * R)
Calculating the value, we find: λ = 4 / (3 * 1.097 × 10^7) λ ≈ 1.215 × 10^-7 meters or 121.5 nm
The transition from n = 2 to n = 1 in the hydrogen atom emits light in the ultraviolet range.
Therefore, the transition from n = 3 to n = 2 emits red light with a wavelength of approximately 65.63 nm, and the transition from n = 2 to n = 1 emits ultraviolet light with a wavelength of approximately 121.5 nm.