Bohr’s quantization condition of angular momentum: According to Bohr, electron can revolve in certain discrete orbits called stationary orbits. The total angular momentum (L) of the revolving electron is integral multiple of h / 2π .
Now, we have that the angular momentum is L = mvr, where m is mass of electron, v is velocity in circular orbit, and R is radius of circular orbit. Therefore,
L = mvr = nh/2π
where n = 1, 2, 3, … is the positive integer and the above condition is Bohr’s quantization condition of angular momentum.
When an electron jumps from on outer stationary orbit to an inner stationary orbit, the difference in the energy is of electron in two orbits is radiated in form of spectral line. Brackett series is obtained when an electron jumps to fourth orbit (n1 = 4) from any outer orbit (n2 = 5, 6, 7, …) of hydrogen atom.
The wavelength of a spectral line is given as
where R is Rydberg’s constant (1.097 107 m−1 ) and Z is atomic number (Z = 1 for hydrogen atom). For Brackett series, n1 = 4 and n2 = 5, 6, 7… Therefore,
For shortest wavelength, n2 = ∞. Therefore,
or λ 1458.5 10-9 m or 1458.5 nm.
The shortest wavelength of the Brackett series is 1458.5 nm.
This wavelength belongs to infrared range of electromagnetic spectrum.
