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Given the value of Rydberg constant is 10⁷ m⁻¹, the wave number of the last line of the Balmer series in hydrogen spectrum will be:

1. 0.025 × 10⁴ m⁻¹
2. 0.5 × 10⁷ m⁻¹
3. 0.25 × 10⁷ m⁻¹
4. 2.5 × 10⁷ m⁻¹

Correct answer: 0.5 × 10⁷ m⁻¹

Solution

The wave number for the last line of the Balmer series corresponds to the transition from n = ∞ to n = 2. Using the formula for wave number, \( \nu = R \left( \frac{1}{2^2} - \frac{1}{\infty^2} \right) \), we get \( \nu = 10^7 \times \frac{1}{4} = 0.5 \times 10^7 \ \text{m}^{-1} \).

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