Consider the following spectral lines for atomic hydrogen : A. First line of Paschen series B. Second line of Balmer series C. Third line of Paschen series D. Fourth line of Bracket series. The correct arrangement of the above lines in ascending order of energy is :
B. D < A < C < B
The energy of a spectral line in the hydrogen atom is given by E = 13.6 ( 1 n_1^2 - 1 n_2^2 ) eV. A. First line of Paschen series: n_1 = 3, n_2 = 4. E_A = 13.6 ( 1 3^2 - 1 4^2 ) = 13.6 ( 1 9 - 1 16 ) = 13.6 7 144 0.66 eV. B. Second line of Balmer series: n_1 = 2, n_2 = 4. E_B = 13.6 ( 1 2^2 - 1 4^2 ) = 13.6 ( 1 4 - 1 16 ) = 13.6 3 16 = 2.55 eV. C. Third line of Paschen series: n_1 = 3, n_2 = 6. E_C = 13.6 ( 1 3^2 - 1 6^2 ) = 13.6 ( 1 9 - 1 36 ) = 13.6 3 36 = 13.6 1 12 1.13 eV. D. Fourth line of Brackett series: n_1 = 4, n_2 = 8. E_D = 13.6 ( 1 4^2 - 1 8^2 ) = 13.6 ( 1 16 - 1 64 ) = 13.6 3 64 0.6375 eV. Comparing the values: E_D (0.6375) The ascending order of energy is D < A < C < B.
Related: Chemistry — Structure of Atom · All PYQ Banks