JEE Mains · Physics · STD 12 - 12. atoms
In a hydrogen like atom electron make transition from an energy level with quantum number \(n\) to another with quantum number \((n- 1)\). If \(n > > 1\), the frequency ofradiation emitted is proportional to
- A \(\frac{1}{{{n^3}}}\)
- B \(\;\frac{1}{n}\)
- C \(\;\frac{1}{{{n^2}}}\)
- D \(\;\frac{1}{{{n^{\frac{3}{2}}}}}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{{{n^3}}}\)
Step-by-step Solution
Detailed explanation
\(\frac{v}{x}=\frac{1}{\lambda}=R Z^{2}\left[\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right]\) \([\because n>>1]\) \(v=R C Z^{2}\left[\frac{1}{(n-1)^{2}}-\frac{1}{n^{2}}\right]\) \(\operatorname{RCZ}^{2}\left[\frac{2 n-1}{n^{2}(n-1)^{2}}\right]\)
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