JEE Advanced 2021 Paper 1 Q14 Physics Modern Physics Bohr Model Hard

JEE Advanced 2021 Paper 1 · Q14 · Bohr Model

Which of the following statement(s) is(are) correct about the spectrum of hydrogen atom?

  1. A. The ratio of the longest wavelength to the shortest wavelength in Balmer series is 9/5
  2. B. There is an overlap between the wavelength ranges of Balmer and Paschen series
  3. C. The wavelengths of Lyman series are given by (1 + 1/m²)λ₀, where λ₀ is the shortest wavelength of Lyman series and m is an integer
  4. D. The wavelength ranges of Lyman series and Balmer series do not overlap
JEE Advanced multi-correct — pick every correct option, then check.
Reveal answer + step-by-step solution

Correct answer:A, D

Solution

Balmer: 1/λ = R(1/4 − 1/n²). Longest (n=3): 1/λ_max = 5R/36 ⇒ λ_max = 36/(5R). Shortest (n=∞): λ_min = 4/R. Ratio = (36/5R)/(4/R) = 9/5 ⇒ (A) correct. Balmer ranges 364.5–656.2 nm; Paschen (n₁=3) ranges 820.2–1874.7 nm — they don't overlap ⇒ (B) wrong. For Lyman, λ = (1 + 1/(n²−1))λ₀; letting m² = n²−1 makes m = √(n²−1), generally irrational ⇒ formula in (C) wrong. Lyman max wavelength 121.5 nm < Balmer min 364.5 nm, so they don't overlap ⇒ (D) correct.

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