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 _________.
Answer (integer)
15
Solution
For 1<sup>st</sup> line<br><br>$${1 \over {{\lambda _1}}} = R{z^2}\left( {{1 \over {{2^2}}} - {1 \over {{3^2}}}} \right)$$<br><br>${1 \over {{\lambda _1}}} = R{z^2}{5 \over {36}}$ ..... (i)<br><br>For 3<sup>rd</sup> line<br><br>$${1 \over {{\lambda _3}}} = R{z^2}\left( {{1 \over {{2^2}}} - {1 \over {{5^2}}}} \right)$$<br><br>${1 \over {{\lambda _3}}} = R{z^2}{{21} \over {100}}$ ...... (ii)<br><br>Dividing (ii) by (i), <br><br>$${{{\lambda _1}} \over {{\lambda _3}}} = {{21} \over {100}} \times {{36} \over 5} = 1.512 = 15.12 \times {10^{ - 1}}$$<br><br>$x \approx 15$
About this question
Subject: Physics · Chapter: Atoms and Nuclei · Topic: Bohr's Model of Hydrogen Atom
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