KCET · Physics · Atomic Physics
\(v_{1}\) is the frequency of the series limit of Lyman series, \(v_{2}\) is the frequency of the first line of Lyman series and \(v_{3}\) is the frequency of the series limit of the Balmer series. Then
- A \(v_{1}-v_{2}=v_{3}\)
- B \(v_{1}=v_{2}-v_{3}\)
- C \(\frac{1}{v_{2}}=\frac{1}{v_{1}}+\frac{1}{v_{3}}\)
- D \(\frac{1}{v_{1}}=\frac{1}{v_{2}}+\frac{1}{v_{3}}\)
Answer & Solution
Correct Answer
(A) \(v_{1}-v_{2}=v_{3}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \text { Frequency, } v &=R C\left[\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right] \\ v_{1} &=R C\left[1-\frac{1}{\infty}\right]=R C \\ v_{2} &=R C\left[1-\frac{1}{4}\right]=\frac{3}{4} R C \\ v_{3} &=R C\left[\frac{1}{4}-\frac{1}{\infty}\right]=\frac{R C}{4} \\ \Rightarrow \quad v_{1}-v_{2}=v_{3} \end{aligned}\)
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