The only electron in the hydrogen atom resides under ordinary conditions on the first orbit. When energy is supplied, the electron moves to higher energy orbit depending on the amount of energy absorbed. When this electron returns to any of the lower orbits, it emits energy. Lyman series is formed when the electron returns to the lowest orbit while Balmer series is formed when the electron returns to second orbit. Similarly, Paschen, Brackett and Pfund series are formed when electron returns to the third, fourth and fifth orbits from higher energy orbits respectively (as shown in figure)

Maximum number of lines produced when electrons jump from n th level to ground level is equal to .

For example, in the case of n = 4, number of lines produced is 6. (4 → 3, 4 → 2, 4 → 1, 3 → 2, 3 → 1, 2 → 1). When an electron returns from n 2 to n 1 state, the number of lines in the spectrum will be equal to

If the electron comes back from energy level having energy E 2 to energy level having energy E 1 , then the difference may be expressed in terms of energy of photon as :

E 2 – E 1 = Δ E, λ = , Δ E = h ν ( ν - frequency)

Since h and c are constants, Δ E corresponds to definite energy; thus each transition from one energy level to another will produce a light of definite wavelength. This is actually observed as a line in the spectrum of hydrogen atom.

Wave number of line is given by the formula .

where R is a Rydberg constant (R = 1.1 × 10 7 m –1 )

(i) First line of a series : It is called ‘line of longest wavelength’ or ‘line of shortest energy’.

(ii) Series limit or last line of a series : It is the line of shortest wavelength or line of highest energy.

(i) Last line of Brackett series for H-atom has wavelength λ 1 Å and 2 nd line of lyman series has wavelength λ 2 Å, then :