The line corresponding to the transition where the electron comes from an infinitely large orbit (n = ∞) to a fixed lower energy level.

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🔹 What it means simply

• When an electron falls from very high energy levels (n = very large), the spectral lines get closer and closer.
• Finally, at n = ∞, they merge into one line → this is the series limit (limiting line).

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🔹 Formula (Rydberg equation)

$\frac{1}{\lambda} = R \left( \frac{1}{n_1^2} – \frac{1}{n_2^2} \right)$

For limiting line$$\frac{1}{\lambda} = \frac{R}{n_1^2}$$

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Examples of limits

1. Lyman series (n₁ = 1)
   • Limit: electron falls from ∞ → 1
   • Region: Ultraviolet (UV)
2. Balmer series (n₁ = 2)
   • Limit: ∞ → 2
   • Region: Visible
3. Paschen series (n₁ = 3)
   • Limit: ∞ → 3
   • Region: Infrared

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Limiting line = shortest wavelength (maximum energy) line of a series.

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Lyman Alpha (α) Line

The Lyman α (alpha) line is the first spectral line of the Lyman series.