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What is the shortest wavelength in the Pfund series of the He+ ion? (R is the Rydberg constant for hydrogen.)

1. 25 / R
2. 4 / R
3. 4R / 25
4. 25 / (4R)

Correct answer: 25 / (4R)

Solution

For He+ (Z=2) and Pfund series (n1=5), the shortest wavelength occurs when the transition is from n2=infinity to n1=5. Using 1/lambda = R*Z²*(1/n1² - 1/n2²) = R*4*(1/25 - 0) = 4R/25. Therefore lambda = 25/(4R).

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