The atomic hydrogen emits a line spectrum consisting of various series. Which series of hydrogen atomic spectra is lying in the visible region?

Solution

Physics sir · 3 steps

Look at the level where the electron lands: only a fall to n = 2 gives photons your eye can see.

1. Series by landing level. Each series is named by the lower level n_f the electron drops to: Lyman (n_f = 1), Balmer (n_f = 2), Paschen (n_f = 3), Brackett (n_f = 4). The wavelength comes from the Rydberg formula.

   1/λ = R(1/n_f² - 1/nᵢ²), 1/R ≈ 91.2 nm

2. Compare with visible. Visible light runs from about 400 nm to 700 nm. A deeper landing level means a bigger energy jump and a shorter wavelength.

   Series	n_f	Wavelength range	Region
   Lyman	1	91–122 nm	ultraviolet
   Balmer	2	365–656 nm	visible
   Paschen	3	820–1875 nm	infrared
   Brackett	4	1460–4050 nm	infrared

3. So. Only the Balmer series falls in the visible band. Its red line at 656 nm (n = 3 → 2) and its blue and violet lines at 486, 434 and 410 nm are all visible, so the answer is (b).

The idea to keep. Remember the order L-B-P-B for n_f = 1, 2, 3, 4: Lyman is ultraviolet, Balmer is visible, and Paschen, Brackett and Pfund are infrared.

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