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Q.

The energy of electron in the nth orbit of hydrogen atom is expressed as $E = \frac{- 13 .6}{n^{2}} eV$ . The shortest and longest wavelength of Lyman series will be

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a

$5463 \overset{0}{A}, 7858 \overset{0}{A}$

b

$1315 \overset{0}{A}, 1530 \overset{0}{A}$

c

$910 \overset{0}{A}, 123 \overset{0}{A}$

d

None of these

answer is A.

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Detailed Solution

$\begin{array}{l} \frac{1}{λ_{\max}} = R [\frac{1}{{(1)}^{2}} - \frac{1}{{(2)}^{2}}] \Rightarrow λ_{\max} = \frac{4}{3 R} \approx 1213 \overset{0}{A} \\ and \frac{1}{λ_{\min}} = R [\frac{1}{{(1)}^{2}} - \frac{1}{\infty}] \Rightarrow λ_{\min} = \frac{1}{R} \approx 910 \overset{0}{A} \end{array}$

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