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Question
Answer in brief.
Solution
For the first line in the Lyman series,
`1/lambda_"L1" = "R"(1/1^2 - 1/2^2) = "R"(1 - 1/4) = "3R"/4`
∴ `"v"_"L1" = "c"/lambda_"L1" = "3Rc"/4`, where v denotes the frequency, c the speed of light in free space and R the Rydberg constant.
For the limit of the Lyman series,
`1/lambda_("L"∞) = "R"(1/1^2 - 1/∞)`= R
∴ `"v"_("L"∞) = "c"/(lambda_"L"∞) = "Rc"`
For the limit of the Balmer series,
`1/lambda_("B"∞) = "R"(1/2^2 - 1/∞) = "R"/4`
∴ `"v"_("B"∞) = "c"/(lambda_"B"∞) = "Rc"/4`
∴ `"v"_("L"∞) - "v"_("B"∞) = "Rc" - "Rc"/4 = "3Rc"/4 = "v"_"L1"`
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