The Lyman series refers to a series of spectral lines in the emission spectrum of hydrogen. These spectral lines are produced when electrons transition from higher energy levels to the ground state in the hydrogen atom. The shortest wavelength of the Lyman series corresponds to the highest energy transition within this series.
The Lyman series is described by the equation:
1/λ = R * (1 - (1/n^2))
Where λ is the wavelength of the spectral line, R is the Rydberg constant (approximately 1.097 × 10^7 m^(-1)), and n is an integer representing the principal quantum number of the energy level the electron transitions from.
The shortest wavelength of the Lyman series corresponds to the highest energy transition, which occurs when the electron transitions from the first excited state (n = 2) to the ground state (n = 1). Plugging these values into the equation, we get:
1/λ = R * (1 - (1/1^2)) = R * (1 - 1) = R * 0
Since anything multiplied by zero is zero, the expression becomes 0. Therefore, the wavelength of the shortest line in the Lyman series is infinite.
In practical terms, this means that the shortest wavelength in the Lyman series lies in the ultraviolet (UV) region of the electromagnetic spectrum, beyond the range of visible light.