Question

In a hydrogen spectrum if an electron moves from 7 to 1 orbit by a transition in multi-steps then find out the total number of lines in the spectrum.

Answer 1

Emission spectrum:

• The wavelengths of the emitted light depend upon the energy difference between the two levels.
• The emission spectrum of a pure sample of Hydrogen gas looks like distinct lines of discrete wavelengths that are absolutely specific to the element hydrogen.
• Some of these lines lie in the visible range of the electromagnetic spectrum, while others lie in the ultraviolet or infrared range.
• This series of spectral emission lines occur when the electron transitions from a high-energy level to a lower energy level.
• The hydrogen spectral lines are Lyman$(n_1=1)$, Balmer series $({\mathrm{n}}_2=2)$, Paschen series$(n_3=3)$, Brackett series $(n_4=4)$, Pfund series $(n_5=5)$ and Humphrey$(n_6=6)$.

Number of lines in the spectrum:

• Lyman

$({\mathrm{n}}_7–n_1)=7–1=6$

• Balmer

$({\mathrm{n}}_7–{\mathrm{n}}_2)=7–2=5$

• Paschen

$(n_7–n_3)=7–3=4$

• Bracket

$({\mathrm{n}}_7–{\mathrm{n}}_4)=7–4=3$

• Pfund

$({\mathrm{n}}_7–{\mathrm{n}}_5)=7–5=2$

• Humphrey

$({\mathrm{n}}_7–{\mathrm{n}}_6)=7–6=1$

The total number of lines is $6+5+4+3+2+1=21$

Hence, the total number of lines in the spectrum is 21.