21 centimeter line
The distances between lines in the hydrogen spectrum decrease with decreasing wavelength because the energy levels in hydrogen are quantized, meaning they can only exist at certain discrete values. As the wavelength decreases, the energy difference between adjacent levels also decreases, resulting in lines being closer together in the spectrum.
The Balmer transition from ( n=4 ) to ( n=2 ) in the hydrogen spectrum corresponds to a wavelength of approximately 486 nm. The transition in the hydrogen spectrum that would have the same wavelength is the transition from ( n=5 ) to ( n=3 ), which also produces a spectral line at around the same wavelength. Both transitions can be calculated using the Rydberg formula for hydrogen spectral lines.
You can calculate the wavelength of light emitted from a hydrogen atom using the Rydberg formula: 1/λ = R(1/n₁² - 1/n₂²), where λ is the wavelength, R is the Rydberg constant, and n₁ and n₂ are the initial and final energy levels of the electron.
Cold atomic hydrogen
410 nanometers is.
The second longest wavelength in the absorption spectrum of hydrogen corresponds to the transition from the n=2 to n=4 energy levels. This transition produces a spectral line known as the H-alpha line, which falls in the red part of the visible spectrum at a wavelength of 656.3 nm.
The n4-n2 transition of hydrogen is in the cyan, with wavelength of 486.1 nm. blue = als
The longest radiation wavelength that can ionize the ground state hydrogen atom is in the ultraviolet range, around 91.2 nm. This is known as the Lyman limit, where the photon energy is just enough to ionize hydrogen by freeing the electron from its bound state.
The wavelength of the hydrogen atom in the 2nd line of the Balmer series is approximately 486 nm. This corresponds to the transition of an electron from the third energy level to the second energy level in the hydrogen atom.
Use the Rydberg formula. A useful article about this is on Wikipedia. It is called "Hydrogen spectral series".
The wavelength of a transition from n=5 to n=3 in hydrogen-like atoms can be calculated using the Rydberg formula: 1/λ = R(1/n₁² - 1/n₂²), where R is the Rydberg constant. The transition will result in the emission of a photon with a wavelength in the ultraviolet region.
The longest wavelength photon I could find out about was in a maser (microwave version of a laser) which uses emission between two hyperfine levels of atomic hydrogen. This had a frequency of 1.4 GHz and a wavelength of 21cm.