Question

If wavelength of the first line of the Paschen series of hydrogen atom is _____ nm, then the wavelength of the second line of this series is nm. (Nearest integer)

Answer 1

$\frac{1}{\left(\lambda_1\right)_{ P }}= R _{ H } Z ^2\left(\frac{1}{9}-\frac{1}{16}\right)$
$\frac{1}{\left(\lambda_2\right)_{ P }}= R _{ H } Z ^2\left(\frac{1}{9}-\frac{1}{25}\right)$
$\frac{\left(\lambda_2\right)_{ P }}{\left(\lambda_1\right)_{ P }}=\frac{\frac{7}{16 \times 9}}{\frac{16}{25 \times 9}}=\frac{25 \times 7}{16 \times 16}$
$\left(\lambda_2\right)_{ P }=\frac{25 \times 7}{16 \times 16} \times 720$
$\left(\lambda_2\right)_{ P }=492 \,nm$