If 917 Aᵒ be the lowest wavelength of Lyman series then the lowest wavelength of Balmer series will be ___________ Aᵒ.

Solution

Physics sir · 3 steps

Lowest wavelength means the series limit, so just compare 1/1² with 1/2².

1. Lowest wavelength. The shortest wavelength in a series has the largest energy jump. That jump is from n₂ = ∞ down to the series' lower level n₁, and it is called the series limit.

   1/λₘᵢₙ = R(1/n₁² - 1/∞²) = R/n₁²

2. Two series. For Lyman, n₁ = 1, so λ_L = 1/R. For Balmer, n₁ = 2, so λ_B = 4/R. Dividing gives λ_B/λ_L = 4.
3. So. λ_B = 4 × 917 = 3668 Å, so the answer is 3668.

The common slip: 6602.4. Taking the first Balmer line (n = 3 → 2) instead of the series limit gives 36/5 × 917 = 6602.4, which is the longest Balmer wavelength, not the lowest.

The idea to keep. The series limit of any hydrogen series is λ = n₁² / R. So series limits scale as n₁², and you never need the value of R.

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