The Pfund series in the hydrogen spectrum corresponds to transitions that have a final state of m=5. A. What are the wavelengths of the first three lines in this series? B. What part of the electromagnetic spectrum are these lines in?

sunnypeach12 2022-08-12 Answered
The Pfund series in the hydrogen spectrum corresponds to transitions that have a final state of m=5.
A. What are the wavelengths of the first three lines in this series? Express your answers in micrometers to three significant figures. Enter your answers in descending order separated by commas.
B. What part of the electromagnetic spectrum are these lines in?
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Answers (1)

afinat4s
Answered 2022-08-13 Author has 13 answers
The wavelength can be calculated using the formula,
1 λ = R h ( 1 5 2 1 n 2 ) n = 6 , 7 , 8 R H = 109677.581   c m 1
The first three wavelengths can be calculated as,
1 λ 1 = 109677.581 ( 1 5 2 1 6 2 ) λ 1 = 7.46 × 10 4   c m = 7.46   μ m 1 λ 2 = 109677.581 ( 1 5 2 1 7 2 ) λ 2 = 4.65   μ m = 1 λ 3 = 109677.581 ( 1 5 2 1 8 2 ) λ 3 = 3.74 × 10 4   c m = 3.74 μ m
These are included in infrared range of electromagnetic spectrum.
The required wavelengths are, 7.46, 4.65 and 3.74 micrometer. They lie in infrared range.

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From my quick investigation, the spectrum is based on the Rydberg formula, and with a small change, would lead to
1 λ μ = m μ m e ( R ( 1 n 1 2 1 n 2 2 ) )
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So, taking hydrogen as an example, we would observe similar bands, shifted into the x-ray/gamma range.
Is this correct?

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