The hydrogen spectrum consists of several spectral lines in Lyman series (L1, L2, L3 ; L1 has lowest energy among Lyman series). Similarly it consists of several spectral lines in Balmer series (B1, B2, B3 ; B1 has lowest energy among Balmer lines). The energy of L1 is x times the energy of B1. The value of x is 10-1. (Nearest integer)
Answer
54
Solution
For hydrogen, E = 13.6 ( 1n12 - 1n22 ) eV
Lowest-energy line of a series is the transition from the next higher level.
L1 (Lyman, 2 1): EL1 112 - 122 = 34
B1 (Balmer, 3 2): EB1 122 - 132 = 536
x = EL1EB1 = 34 365 = 275 = 5.4 = 54 10-1
Answer: 54