In the line spectra of hydrogen atom, difference between the...

\dfrac{1}{{\lambda}_\min} = R\left(1\right) = R; n = \infty to $1$

\dfrac{1}{{\lambda}_\max} = R\left\{1 - \dfrac{1}{4}\right\} = \dfrac{3R}{4} ; $n = 2$ to $1$

$⇒$ {\lambda}_\max - {\lambda}_\min = \dfrac{4}{3R} - \dfrac{1}{R}

$304 = \dfrac{1}{3R}$ ......\left(a\right)$</p><p>Paschen :${Y}_{\lambda{'}_\min} = R\left(\dfrac{1}{9}\right)$</p><p>and${Y}_{\lambda{'}_\max} = R\left(\dfrac{1}{9} - \dfrac{1}{16}\right) = \dfrac{7R}{16 \times 9}$</p><p>${\lambda}^{'}max - {\lambda}^{'}min = \dfrac{16 \times 9}{7R} - \dfrac{9}{R} = \dfrac{81}{7R}$...\left(b\right)$

$\dfrac{\left(b\right)}{\left(a\right)} = \dfrac{x}{3 \times 304} = \dfrac{81}{7}$

$⇒$ $x = 10553 . 14$