The wavelengths of Kα X-rays for lead isotopes Pb208, Pb206, and Pb204 are λ₁, λ₂, and λ₃ respectively. Then λ₂ = ?

Wavelengths of Kα lines for given isotopes of lead can be given by a general expression
1λ=R(Z−1)²(11²−12²)
Where, R is Rydberg's constant, Z is atomic number of the isotopes (Z will be same for all the three isotopes, i.e 82)
1λ₁=R(82−1)²(11²−12²)=34R(81)²
Similarly, 1λ₂=1λ₃=34R(81)²
⇒(1λ₂)²=1λ₁×1λ₃
⇒λ₂=√λ₁λ₃