JEE Mains · Physics · STD 12 - Atoms
- JEE Mains 2021
- Hard
- Numerical
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
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(15\)
Step-by-step Solution
Detailed explanation
For 1 st line
\(\frac{1}{\lambda_{1}}= R z^{2}\left(\frac{1}{2^{2}}-\frac{1}{3^{2}}\right)\)
\(\frac{1}{\lambda_{1}}= R z^{2} \frac{5}{36}\) ........\((i)\)
For \(3^{\text {rd }}\) line
\(\frac{1}{\lambda_{3}}= Rz ^{2}\left(\frac{1}{2^{2}}-\frac{1}{5^{2}}\right)\)
\(\frac{1}{\lambda_{3}}= Rz ^{2} \frac{21}{100}\) \(.........(ii)\)
(ii) \(+( i )\)
\(\frac{\lambda_{1}}{\lambda_{3}}=\frac{21}{100} \times \frac{36}{5}=1.512=15.12 \times 10^{-1}\)
\(x \approx 15\)
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