Question

If ${\lambda }_1$ and ${\lambda }_2$ are respectively the wavelengths of the series limit of Lyman and Balmer series of Hydrogen atom, then the wavelength of the first line of the Lyman series of the H-atom is:

• A. ${\lambda }_1-{\lambda }_2$
• B. $\sqrt{{\lambda }_1{\lambda }_2}$
• C. $\frac{{\lambda }_2-{\lambda }_1}{{\lambda }_1{\lambda }_2}$
• D. $\frac{{\lambda }_1{\lambda }_2}{{\lambda }_2-{\lambda }_1}$

Answer 1

The correct option is D

$\frac{{\lambda }_1{\lambda }_2}{{\lambda }_2-{\lambda }_1}$

(i) Series limit of Lyman series $\Rightarrow n=\infty ton=1$.
(ii) Series limit of Balmer series $\Rightarrow n=\infty ton=2$.
$E_{n=2ton=1}=E_{n=\infty ton=1}-E_{n=\infty ton=2}$
$\frac{hC}{\lambda }=\frac{hC}{{\lambda }_1}-\frac{hC}{{\lambda }_2}$
$\frac{1}{\lambda }=\frac{1}{{\lambda }_1}-\frac{1}{{\lambda }_2}\Rightarrow \lambda =\frac{{\lambda }_1{\lambda }_2}{{\lambda }_2-{\lambda }_1}$