MHT CET · Physics · Atomic Physics
Electron in Hydrogen atom first jumps from third excited state to second excited
state and then from second excited state to first excited state. The ratio of the
wavelengths \(\lambda_{1}: \lambda_{2}\) emitted in the two cases respectively is
- A \(\frac{7}{5}\)
- B \(\frac{27}{20}\)
- C \(\frac{27}{5}\)
- D \(\frac{20}{7}\)
Answer & Solution
Correct Answer
(D) \(\frac{20}{7}\)
Step-by-step Solution
Detailed explanation
\(\frac{1}{\lambda_{1}}=\mathrm{R}\left(\frac{1}{2^{2}}-\frac{1}{3^{2}}\right)=\mathrm{R}\left(\frac{1}{4}-\frac{1}{9}\right)=\mathrm{R}\left(\frac{5}{36}\right)\)
\(\frac{1}{\lambda_{2}}=\mathrm{R}\left(1-\frac{1}{2^{2}}\right)=\mathrm{R}\left(\frac{3}{4}\right)\)
\(\frac{\lambda_{1}}{\lambda_{2}}=\frac{3}{4} \times \frac{36}{5}=\frac{27}{5}\)
\(\frac{1}{\lambda_{2}}=\mathrm{R}\left(1-\frac{1}{2^{2}}\right)=\mathrm{R}\left(\frac{3}{4}\right)\)
\(\frac{\lambda_{1}}{\lambda_{2}}=\frac{3}{4} \times \frac{36}{5}=\frac{27}{5}\)
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