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QPages 382-383: Q1: HC Verma: Concepts of Physics - Volume 2 Bohr's Model and Physics of the Atom Pages 382-383: Q1 Solution: How many wavelengths are emitted by atomic hydrogen in visible…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently equate the Balmer series limit (≈364.6 nm) with the visible lower bound and count only the first few lines, overlooking that higher‑n transitions (n=7,8,9,10…) still have λ > 380 nm and belong in the visible range; always compute each wavelength and verify it lies within the specified interval, and do the same check for the Lyman lines in the 50‑100 nm window.

How many wavelengths are emitted by atomic hydrogen in visible range 380 nm _ 780 nm)? In the range 50 nm to 100 nm?

Step-by-Step Verified Solution

**Answer:** Number of wavelengths in visible range: 4. Number in the range 50 nm to 100 nm: 1. **Step-by-Step Explanation:** For hydrogen, the visible range is the Balmer series (n_ = 2). The wavelengths are given by:
1λ=R(122−1n22)\frac{1}{\lambda} = R\left(\frac{1}{2^2} - \frac{1}{n_2^2}\right)
For n_ = 3, 4, 5, 6... the wavelengths are 656 nm, 486 nm, 434 nm, 410 nm, etc. The Balmer series converges to 364.6 nm. All these lie in the visible range (380�780 nm). The lines with n_ > 6 fall below 380 nm, so 4 lines are visible [citation:14]. For the range 50�100 nm (Lyman series, n_ = 1), the wavelengths are:
1λ=R(1−1n22)\frac{1}{\lambda} = R\left(1 - \frac{1}{n_2^2}\right)
For n_ = 2: _ = 121.5 nm (outside 50�100). For n_ = 3: _ = 102.5 nm. For n_ = 4: _ = 97.2 nm. So only one line (n_ = 3, _ = 102.5 nm) lies in the 50�100 nm range.

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