2. structure of atom — Chemistry STD 11 Science — Question

For Lyman series,

$n_{1}=1$ and $\lambda$ is shortest if $n_{2}=\infty$

$\therefore R_{\mathrm{H}}=\frac{1}{\mathrm{x}},$ for $\mathrm{H}-$ atom $(Z=1)$

For Balmer series,

$n_{1}=2$ and $\lambda$ is longest if $n_{2}=3$

$\text { (For } \mathrm{He}^{+} \text {ion } \left.Z=2\right)$

$\frac{1}{\lambda_{\max }}=R_{H}(2)^{2}\left[\frac{1}{2^{2}}-\frac{1}{3^{2}}\right]$

$=\frac{1}{x} \times 4\left[\frac{5}{36}\right]$

$\lambda_{\max }=\frac{9 x}{5}$