The shortest wavelength of the spectral lines in the Lyman series of hydrogen spectrum is 915Aᵒ. The longest wavelength of spectral lines in the Balmer series will be _______ Aᵒ.

Solution

Physics sir · 4 steps

The Lyman series limit gives you 1/R directly. Then the Balmer longest line is just a ratio.

1. Lyman limit. The shortest Lyman line is the jump from n = ∞ to n = 1, so 1/λ = R(1/1² - 0) = R. That means 1/R = 915 Å.
2. Longest Balmer line. The longest wavelength means the smallest energy gap. In the Balmer series that is the jump from n = 3 to n = 2.

   1/λ = R(1/2² - 1/3²) = 5R/36

3. Put in numbers. λ = 36/5 × 1/R = 36/5 × 915 Å = 36 × 183 Å.
4. So. The longest Balmer wavelength is 6588 Å.

The common slip: 3660. Using the Balmer series limit (n = ∞ to n = 2) instead of n = 3 to n = 2 gives 4 × 915 = 3660 Å, which is the shortest Balmer line, not the longest.

The idea to keep. Shortest line of a series means the jump from n = ∞. Longest line means the jump from the very next level. Compare any two lines through the ratio of their (1/n₁² - 1/n₂²) factors.

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