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QPages 382-383: Q7: HC Verma: Concepts of Physics - Volume 2 Bohr's Model and Physics of the Atom Pages 382-383: Q7 Solution: The difference in the frequencies of series limit of Lyman…

The difference in the frequencies of series limit of Lyman series and Balmer series is equal to the frequency of the first line of the Lyman series. Explain.

Step-by-Step Verified Solution

**Answer:** The difference in frequencies of the series limits of Lyman and Balmer series equals the frequency of the first line of the Lyman series. **Step-by-Step Explanation:** Series limit of Lyman: n = � _ 1, frequency νL,∞=Rc(1/12−0)=Rc\nu_{L,\infty} = Rc(1/1^2 - 0) = Rc. Series limit of Balmer: n = � _ 2, frequency νB,∞=Rc(1/22−0)=Rc/4\nu_{B,\infty} = Rc(1/2^2 - 0) = Rc/4. Difference: νL,∞−νB,∞=Rc−Rc/4=3Rc/4\nu_{L,\infty} - \nu_{B,\infty} = Rc - Rc/4 = 3Rc/4. First line of Lyman: n = 2 _ 1, frequency νL,1=Rc(1/12−1/22)=3Rc/4\nu_{L,1} = Rc(1/1^2 - 1/2^2) = 3Rc/4. Hence, the difference equals the frequency of the first Lyman line [citation:3].

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