Which absorption line in the hydrogen spectrum occurs at the highest frequency?
The correct answer and explanation is:
The absorption line in the hydrogen spectrum that occurs at the highest frequency is the Lyman series‘ Lyman-alpha line.
In the hydrogen spectrum, various series of lines correspond to electron transitions between energy levels. These lines are classified into different series: the Lyman series, Balmer series, Paschen series, Brackett series, and Pfund series, based on the energy levels involved in the transition.
The Lyman series is the highest-energy series, as it involves transitions of electrons to the n=1 energy level, which is the lowest energy state of the hydrogen atom. The Lyman-alpha line, specifically, corresponds to the transition from the n=2 level to the n=1 level. Since this transition involves the largest difference in energy levels compared to other series, it results in the highest frequency (and hence the shortest wavelength) in the hydrogen spectrum.
The relationship between frequency, energy, and wavelength is governed by the equation: E=hνE = h \nu
where EE is the energy of the photon, hh is Planck’s constant, and ν\nu is the frequency. The frequency is inversely proportional to the wavelength, so higher energy transitions result in higher frequencies and shorter wavelengths.
In terms of the electromagnetic spectrum, the Lyman-alpha line falls in the ultraviolet (UV) range, with a wavelength of approximately 121.6 nm. This high frequency is a result of the large energy gap between the n=1 and n=2 levels, making the Lyman-alpha transition the highest-frequency absorption line in the hydrogen spectrum. This is significant because UV light carries enough energy to excite hydrogen atoms, enabling such transitions.