If-1-and-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-1-1-

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Question Number 15906 by Tinkutara last updated on 15/Jun/17

$$\mathrm{If}{\lambda }_1\mathrm{and}{\lambda }_2\mathrm{are}\mathrm{respectively}\mathrm{the}$$$$\mathrm{wavelengths}\mathrm{of}\mathrm{the}\mathrm{series}\mathrm{limit}\mathrm{of}\mathrm{Lyman}$$$$\mathrm{and}\mathrm{Balmer}\mathrm{series}\mathrm{of}\mathrm{Hydrogen}\mathrm{atom},$$$$\mathrm{then}\mathrm{the}\mathrm{wavelength}\mathrm{of}\mathrm{the}\mathrm{first}\mathrm{line}\mathrm{of}$$$$\mathrm{the}\mathrm{Lyman}\mathrm{series}\mathrm{of}\mathrm{the}\mathrm{H}-\mathrm{atom}\mathrm{is}$$$$\left(1\right){\lambda }_1-{\lambda }_2$$$$\left(2\right)\sqrt{{\lambda }_1{\lambda }_2}$$$$\left(3\right)\frac{{\lambda }_2-{\lambda }_1}{{\lambda }_1{\lambda }_2}$$$$\left(4\right)\frac{{\lambda }_1{\lambda }_2}{{\lambda }_2-{\lambda }_1}$$

Answered by ajfour last updated on 15/Jun/17

$$\frac{1}{{\lambda }_1}=R,\frac{1}{{\lambda }_2}=R/4,\frac{1}{{\lambda }_{L1}}=\frac{3R}{4}$$$$As\frac{3R}{4}=R-\frac{R}{4}$$$$\frac{1}{{\lambda }_{L1}}=\frac{1}{{\lambda }_1}-\frac{1}{{\lambda }_2}$$$$\Rightarrow {\lambda }_{L1}=\frac{{\lambda }_1{\lambda }_2}{{\lambda }_2-{\lambda }_1}.option\left(4\right).$$

Commented by Tinkutara last updated on 15/Jun/17

$$\mathrm{Thanks}\mathrm{Sir}!$$

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