If λ₁ and λ₂ are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of λ₁ : λ₂ is :

Solution

Physics sir · 4 steps

Name the jump for each line first: third Lyman member is 4 to 1, first Paschen member is 4 to 3.

1. Identify the transitions. Lyman lines end on n = 1, so its members start at n = 2, 3, 4, … and the third member is 4 → 1. Paschen lines end on n = 3, so the first member is 4 → 3.

   1/λ = R(1/n₁²-1/n₂²)

2. Each wavelength. For Lyman: 1/λ₁ = R(1-1/16) = 15R/16. For Paschen: 1/λ₂ = R(1/9-1/16) = 7R/144.
3. Take the ratio. Wavelength is the reciprocal, so λ₁/λ₂ = (7R/144)/(15R/16) = (7 × 16)/(144 × 15) = 7/135.
4. So. λ₁ : λ₂ = 7 : 135, which is option (a).

The idea to keep. The k-th member of a series starts k levels above the series' lower level. Fix both levels first, then use the Rydberg formula, and remember that a larger 1/λ means a shorter wavelength.

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