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The first three spectral lines of H-atom in the Balmer series are given \lambda _{1},\lambda _{2},\lambda _{3} considering the Bohr atomic model, the wave lengths of first and third spectral lines \left ( \frac{\lambda _{1}}{\lambda _{3}} \right ) are related by a factor of approximately 'x' \times 10^{-1}. The value of x, to the nearest integer, is ___________.
Option: 1 15
Option: 2 30
Option: 3 45
Option: 4 60

Answers (1)

best_answer

For 1st line
\frac{1}{\lambda_{1}}=\mathrm{Rz}^{2}\left(\frac{1}{2^{2}}-\frac{1}{3^{2}}\right)

\Rightarrow \frac{1}{\lambda_{1}}=\mathrm{Rz}^{2}\times \frac{5}{36} \quad......(i)

For 3rd line
\\\frac{1}{\lambda_{3}}=\mathrm{Rz}^{2}\left(\frac{1}{2^{2}}-\frac{1}{5^{2}}\right)\\ \Rightarrow \frac{1}{\lambda_{3}}=\mathrm{Rz}^{2}\times \frac{21}{100} \quad \ldots \ldots (ii)
From equation (i) and (ii)
\\\frac{\lambda_{1}}{\lambda_{3}}=\frac{21}{100} \times \frac{36}{5}=1.512=15.12 \times 10^{-1} \\\\ \Rightarrow \mathrm{x} \approx 15

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avinash.dongre

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