In hydrogen spectrum, the shortest wavelengths of Lyman and Balmer series are ₁ and ₂ respectively. The Rydberg constant of hydrogen is

Step-by-step solution

For Lymen series aligned & 1 ₁ = R _ H [ 1 n ₁^2 - 1 n ₂^2 ] & n ₁=1 and n ₂= aligned 1 ₁ = R _ H ...(1) For balmer series aligned & 1 ₂ = R _ H [ 1 n ₁^2 - 1 n ₂^2 ] & n ₁=2 and n ₂= aligned 1 ₂ = R _ H 4 ...(2) aligned & 1 ₂ - 1 ₁ = R _ H 4 - R _ H & ₁- ₂ ₁ ₂ = -3 R _ H 4 aligned Rydberg constant, R _ H = 4 ( ₂- ₁ ) 3 ₁ ₂