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पाठ्यक्रम

The Line Spectra of the Hydrogen Atom

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Estimated time: 8 minutes
CBSE: Class 12

Formula: Spectral Series

General Formula for all Spectral Series:

\[\frac{1}{\lambda}=R\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right]\]

where \[R=1.097\times10^7\mathrm{m}^{-1},n_1=\text{final state},n_2=\text{initial state},n_2>n_1\]

Series Final State (n₁) Formula
Lyman n₁ = 1 \[\frac{1}{\lambda}=R\left[\frac{1}{1^2}-\frac{1}{n_2^2}\right]\]
Balmer n₁ = 2 \[\frac{1}{\lambda}=R\left[\frac{1}{2^2}-\frac{1}{n_2^2}\right]\]
Paschen n₁ = 3 \[\frac{1}{\lambda}=R\left[\frac{1}{3^2}-\frac{1}{n_2^2}\right]\]
Brackett n₁ = 4 \[\frac{1}{\lambda}=R\left[\frac{1}{4^2}-\frac{1}{n_2^2}\right]\]
Pfund n₁ = 5 \[\frac{1}{\lambda}=R\left[\frac{1}{5^2}-\frac{1}{n_2^2}\right]\]
CBSE: Class 12

Key Points: The Line Spectra of the Hydrogen Atom

  • Lyman series — n₁=1, n₂: 2→∞; converges toward 91–122 nm; UV region
  • Balmer series — n₁=2, n₂: 3→∞; converges toward 365–657 nm; visible region (Hα = Red, Hβ = Blue-green, Hγ = Blue)
  • Paschen series — n₁=3, n₂: 4→∞; converges toward 821–1876 nm; infrared (IR)
  • Brackett series — n₁=4, n₂: 5→∞; converges toward 1459–4053 nm; IR region
  • Pfund series — n₁=5, n₂: 6→∞; converges toward 2280–7462 nm; IR region
  • Humphreys series — n₁=6, n₂: 7→∞; converges toward 3283 nm–∞; IR region
  • Setting n₁=1 and n₂ from 2 to ∞ gives the Lyman series converging to 91 nm

Related QuestionsVIEW ALL [44]

The first excited energy of a He+ ion is the same as the ground state energy of hydrogen. Is it always true that one of the energies of any hydrogen-like ion will be the same as the ground state energy of a hydrogen atom?

The average kinetic energy of molecules in a gas at temperature T is 1.5 kT. Find the temperature at which the average kinetic energy of the molecules of hydrogen equals the binding energy of its atoms. Will hydrogen remain in molecular from at this temperature? Take k = 8.62 × 10−5 eV K−1.

A hydrogen atom in ground state absorbs 10.2 eV of energy. The orbital angular momentum of the electron is increased by

Let An be the area enclosed by the nth orbit in a hydrogen atom. The graph of ln (An/A1) against ln(n)

(a) will pass through the origin
(b) will be a straight line with slope 4
(c) will be a monotonically increasing nonlinear curve
(d) will be a circle

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(a) Find the first excitation potential of He+ ion. (b) Find the ionization potential of Li++ion.

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When a photon is emitted from an atom, the atom recoils. The kinetic energy of recoil and the energy of the photon come from the difference in energies between the states involved in the transition. Suppose, a hydrogen atom changes its state from n = 3 to n = 2. Calculate the fractional change in the wavelength of light emitted, due to the recoil.

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