Physics · Atoms · NEET
Balmer lines are in the VISIBLE region (about 400 to 700 nm). This is the one hydrogen series your eye can actually see. Only the far end of the series (the series limit near 365 nm) slips just into the near-ultraviolet. Do not confuse it with the Lyman series, which is fully ultraviolet.
Each series is named by the LOWER level the electron lands on. Balmer is defined as all jumps that finish at n = 2. Jumps that finish at n = 1 form a different series (Lyman). So n = 2 is the fixed floor for Balmer; the upper level n2 can be 3, 4, 5 and so on.
The longest wavelength comes from the SMALLEST energy jump, which is n = 3 to n = 2. This is the H-alpha line at 656.3 nm (red light). Rule: smallest jump = smallest energy = longest wavelength = first line of the series.
The shortest wavelength is the series limit, from n = infinity to n = 2. Using 1/lambda = R(1/4 - 0) = R/4, with R = 1.097 x 10^7 per metre, lambda = about 365 nm. This is the largest energy jump, so shortest wavelength and the last line of the series.
Balmer lands on n = 2 and is visible; Lyman lands on n = 1 and is ultraviolet. Lyman jumps involve bigger energy gaps (electron falls all the way to the ground state), so Lyman photons carry more energy and have shorter wavelengths than Balmer photons.
The n = 3 to n = 2 transition gives H-alpha at 656.3 nm, which appears red. The next lines are H-beta (n=4 to 2, 486.1 nm, blue-green), H-gamma (n=5 to 2, 434.1 nm, violet) and H-delta (n=6 to 2, 410.2 nm, violet).
Given the value of Rydberg constant is 10^7 per metre, the wave number of the last line of the Balmer series in hydrogen spectrum will be:
In hydrogen spectrum, the shortest wavelength in the Balmer series is lambda. The shortest wavelength in the Brackett series is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
1/lambda = R(1/2^2 - 1/n2^2), where n2 = 3, 4, 5... and R = 1.097 x 10^7 per metre. The lower level is fixed at n1 = 2 for every Balmer line.
In theory an infinite number, because n2 can be 3, 4, 5 and so on up to infinity. The lines crowd closer together as they approach the series limit near 365 nm.
Balmer jumps end at n = 2, giving medium-sized energy gaps whose photons have wavelengths of about 400 to 700 nm, which is exactly the visible range. Lyman (ending at n = 1) is higher energy and ultraviolet; Paschen, Brackett and Pfund end at n = 3 or higher and are infrared.
The first line is H-alpha, the n = 3 to n = 2 transition at 656.3 nm (red). It is the smallest energy jump in the series, so it has the longest wavelength.
It can appear in both. In emission the electron falls from a higher level to n = 2 and gives out a photon. In absorption an electron already in n = 2 absorbs a photon and jumps up, so the same wavelengths appear as dark lines.
