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In Bohr's model, what is the wave number for the final spectral line in the Balmer series of hydrogen?

1. 1 / λ = RZ² [1 / n₁² - 1 / n₂²]
2. 1 / λ = R [1 / 4 - 1 / ∞]
3. Wave number = 0.25 × 10⁷ m⁻¹
4. None of these

Correct answer: 1 / λ = R [1 / 4 - 1 / ∞]

Solution

The last line of the Balmer series corresponds to the transition from n₂ = ∞ to n₁ = 2. Using the formula 1/λ = R [1/n₁² - 1/n₂²], substituting n₁ = 2 and n₂ = ∞ gives 1/λ = R [1/2² - 0] = R/4.

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