Chemistry - Atomic Structure Question with Solution | TestHub

For Hydrogen atom ($\mathrm{H}$) ($\mathrm{Z} = 1$) : ${\left(\frac{1}{\mathrm{\lambda }}\right)}_{\mathrm{H}}={\mathrm{R}}_{\mathrm{H}}\times 1^2\left[\frac{1}{1^2}-\frac{1}{{\infty }^2}\right]$ ...(1)

For ${\mathrm{He}}^{+}$ atom ($\mathrm{Z} = 2$) : ${\left(\frac{1}{\mathrm{\lambda }}\right)}_{{\mathrm{He}}^{+}}={\mathrm{R}}_{\mathrm{H}}\times 2^2\times \left[\frac{1}{2^2}-\frac{1}{3^2}\right] = {\mathrm{R}}_{\mathrm{H}} \left[1 - \frac{4}{9}\right] = {\mathrm{R}}_{\mathrm{H}} \left(\frac{5}{9}\right)$ ..(2)

From (1) & (2)

$\frac{{\lambda }_{{\mathrm{He}}^{+}}}{{\lambda }_{\mathrm{H}}}=\frac{9}{5}$

${\lambda }_{{\mathrm{He}}^{+}}=\lambda \times \frac{9}{5}$

${\lambda }_{{\mathrm{He}}^{+}}=\frac{9\lambda }{5}$.