In the hydrogen atom, the wavelength of light emitted during a transition can be calculated using the Rydberg formula:
1/λ = R * (1/n₁² - 1/n₂²)
Where: λ is the wavelength of the emitted light, R is the Rydberg constant (approximately 1.097 × 10^7 m⁻¹), n₁ is the initial energy level (principal quantum number) of the electron, and n₂ is the final energy level (principal quantum number) of the electron.
Let's calculate the wavelength and identify the type of electromagnetic radiation emitted in each transition:
Transition: n = 3 to n = 2
Using the Rydberg formula:
1/λ = R * (1/2² - 1/3²) 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 wavelength:
λ = 36/(5 * 1.097 × 10^7 m⁻¹) λ ≈ 6.56 × 10^(-7) m (or 656 nm)
The light emitted during this transition has a wavelength of approximately 656 nanometers (nm) and corresponds to red light in the visible spectrum.
Therefore, the transition n = 3 to n = 2 in the hydrogen atom emits red light.
It's worth noting that the above calculations assume hydrogen as a single electron system. In more complex atoms or ions, additional factors need to be considered, such as electron-electron interactions and fine structure effects, which can slightly modify the transition wavelengths.