JEE Main 2024 · 6 April · evening · Single correct · +4 / −1

The longest wavelength associated with Paschen series is : (Given R_H=1.097 × 10⁷ SI unit)

  1. (a) 2.973 × 10⁻⁶ m
  2. (b) 1.876 × 10⁻⁶ m
  3. (c) 1.094 × 10⁻⁶ m
  4. (d) 3.646 × 10⁻⁶ m
Answer and solution

Answer (b) 1.876 × 10⁻⁶ m

Solution

Physics sir · 3 steps

Longest wavelength means smallest energy jump, so take the nearest level above n = 3: the 4 to 3 drop.

  1. Paschen series. Every Paschen line ends on n = 3. Since λ goes as 1/Δ E, the longest wavelength comes from the smallest energy gap. That is the jump from n = 4 to n = 3.

    1/λ = R_H(1/3²-1/4²) = R_H(1/9-1/16) = 7R_H/144

  2. Put in numbers. λ = 144/7R_H = 144/(7 × 1.097 × 10⁷) m = 144/(7.679 × 10⁷) m ≈ 1.875 × 10⁻⁶ m.
  3. So. The longest Paschen wavelength is about 1.876 × 10⁻⁶ m, which is option (b).

The idea to keep. For any series, the longest wavelength is the jump from the very next level down to the series' final level. The shortest wavelength, the series limit, comes from n = ∞.

Answer from the NTA final answer key. Solution by PrepWiser.

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Asked about 110 times in JEE Main since 2020. This question is from 2024.