If R is Rhydberg constant and longest wavelength of Paschen series is α/7R then α is ____ ?

Question

If R is Rhydberg constant and longest wavelength of Paschen series is \(\frac \alpha {7R}\) then α is ____ ?

Answer 1

1st line of Paschen series is: n₂ = 4 → n₁ = 3

\(\frac 1\lambda = R.Z^2 \left( \frac 1{{n_1}^2 } - \frac 1{{n_2}^2}\right)\)

\(\Rightarrow\frac 1\lambda = R.(1)^2 \left( \frac 1{{3}^2 } - \frac 1{{4}^2}\right)\)

\(\Rightarrow\frac 1\lambda =\frac {7R}{144}\)

\(\Rightarrow \lambda = \frac{144}{7R}\)

\(\therefore \alpha = 144\)