For Lyman series, n1=1.
For shortest wavelength in Lyman series (i.e., series limit), the energy difference in two states showing transition should be maximum, i.e., n2=∞.
1/λ = R(1(n1)2−1/(n2)2) ⋅ Z2
R = Rydbergs constant (Also written is RH)
Z = atomic number.
since the electron is de-exited from 1(st) exited state (i.e n=2) to ground state (i.e n=1) for first line of Lyman series.
1/λ = R(1(1)2−1/(2)2) ⋅ Z2
Since the atomic number of Hydrogen is 1.
λ = 4/3⋅912 A.
1/R = 912 A.
λ = 121.6nm