Chemistry - Atomic Structure Question with Solution | TestHub

$\frac{1}{\mathrm{\lambda }}={\mathrm{R}}_{\mathrm{H}}\times {\left(\mathrm{Z}\right)}^2 \left(\frac{1}{{\mathrm{n}}_1^2}-\frac{1}{{\mathrm{n}}_2^2}\right)$

Shortest wavelength for Lyman series of$\mathrm{H} \mathrm{atom}$

${\mathrm{n}}_1=1$(Lyman series)

${\mathrm{n}}_2=\infty$

SO,$\frac{1}{{\mathrm{\lambda }}_1}=1\times {\mathrm{R}}_{\mathrm{H}}\left(\frac{1}{1}-\frac{1}{\mathrm{\infty }}\right)$

${\mathrm{\lambda }}_1=\frac{1}{{\mathrm{R}}_{\mathrm{H}}}=\mathrm{A} \therefore \mathrm{\lambda }=\mathrm{A}$

longest wavelength for Paschen series of${\mathrm{He}}^{+}$atom

${\mathrm{n}}_1=3$

${\mathrm{n}}_2=4$

$\frac{1}{{\mathrm{\lambda }}_2}={\left(2\right)}^2\times {\mathrm{R}}_{\mathrm{H} }\left(\frac{1}{{\left(3\right)}^2}-\frac{1}{{\left(4\right)}^2}\right)$

$\frac{1}{{\mathrm{\lambda }}_2}=4\times {\mathrm{R}}_{\mathrm{H} }\left(\frac{7}{9\times 16}\right)=\frac{\mathrm{R}\times 7}{36}$

${\mathrm{\lambda }}_2=\frac{36}{7{\mathrm{R}}_{\mathrm{H}}}=\frac{36}{7}\mathrm{A}$.