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Question
Calculate the wavelength for the first three lines in the Paschen series.
(Given RH =1.097 ×107 m-1)
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Solution
Given:
RH = 1.097 × 107 m−1,
For Paschen series, n = 3,
To find: Wavelength of first three lines of Paschen series
Formula:
For the Paschen series, `1/lambda = "R"_"H"(1/3^2 - 1/"m"^2)`
Calculation:
For the first line of the Paschen series,
From the formula,
`1/lambda = 1.097 xx 10^7 (1/3^2 - 1/4^2)`
= `1.097 × 10^7 × (7/(9 xx 16))`
= 0.05333 × 107 m−1
Using the reciprocal table,
λ1 = 1.876 × 10−6 m
For the second line of the Paschen series,
From formula,
`1/lambda_2 = 1.097 xx 10^7 (1/3^2 - 1/5^2)`
`= 1.097 × 10^7 × (16/(9 xx 25))`
= 0.075 × 107 m−1
Using the reciprocal table,
λ2 = 1.282 × 10−6 m
For the third line of the Paschen series,
From formula,
`1/lambda_3 = 1.097 xx 10^7 (1/3^2 - 1/6^2)`
= `1.097 xx 10^7 xx (27/(9 xx 36))`
= 0.0914 × 107 m−1
Using the reciprocal table,
`lambda_3` = 1.094 × 10-6 m
The wavelength of the first three lines of the Paschen series is 1.876 × 10−6 m, 1.282 × 10−6 m, 1.094 × 10-6 m, respectively.
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