The region in the electromagnetic spectrum where the Balmer series lines appear is:

🧠 The Thermal Threshold Hydrogen's electrons are locked in specific shells. When they drop to the second shell ($n=2$), the energy they release falls into a very narrow window of the electromagnetic spectrum. It's the only series that our eyes can actually see without help!

🗺️ The Wavelength Range

1. The Shortest (Limit): $n = \infty \to 2$. $\lambda \approx \frac{1}{R(1/4)} = \frac{4}{1.097 \times 10^7} \approx 364.6 \text{ nm (Near UV)}$
2. The Longest ($H_\alpha$): $n = 3 \to 2$. $\lambda = \frac{1}{R(1/4 - 1/9)} = \frac{36}{5R} \approx 656.3 \text{ nm (Deep Red)}$
3. The Conclusion: The span of $364$ nm to $656$ nm covers almost the entire Visible spectrum (the "VIBGYOR" range).

⚡ The "Rule of Thumb"

• Lyman: UV (Ends at 1, High Energy)
• Balmer: Visible (Ends at 2, Moderate Energy)
• Paschen/Brackett/Pfund: Infrared (Ends at 3+, Low Energy)

⚠️ Common Traps Technically, the very last lines of the Balmer series (like $\infty \to 2$) are in the near-ultraviolet. However, for JEE and textbook purposes, Balmer is almost always categorized as the Visible series.

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