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What is the wavelength λ for the final transition in the Balmer series, where the initial energy level is n₁ = 2 and the final energy level is n₂ = ∞?

1. λ = RZ² [1 / n₁² - 1 / n₂²]
2. λ = R [1 / 2² - 1 / ∞²]
3. λ = 4 / R
4. None of these

Correct answer: λ = 4 / R

Solution

The Balmer series corresponds to transitions ending at n₁ = 2. For the last line, n₂ = ∞. Using the formula for wavelength, 1/λ = R [1/n₁² - 1/n₂²], substituting n₁ = 2 and n₂ = ∞ gives 1/λ = R [1/2² - 0] = R/4, so λ = 4/R.

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