Question

hv = E₀ $\left[\frac{1}{n_1^2}-\frac{{\displaystyle 1}}{{\displaystyle n_2^2}}\right]$
for Lyman series for series limit n₂ = $\infty$, n₁ = 1
hv_L = E₀[1]         ...(1)
for p-fund series
for series limit n₂ = $\infty$, n₁ = 5
hv_p = E₀ $\left[\frac{1}{25}\right]$   ...(2)
By dividing equation (1) and (2)
$\frac{v_L}{v_p}=\frac{25}{1}\Rightarrow$ v_p = v_L/25