Q1. Find the energy released when an electron jumps from n = 3 to n = 2 in hydrogen.
E₃ = −13.6/9 = −1.51 eV; E₂ = −13.6/4 = −3.4 eV
ΔE = E₂ − E₃... energy emitted = E₃ − E₂ = −1.51 − (−3.4)
ΔE = 1.89 eV (a red line of the Balmer series)
Atoms — Class 12
Bohr's model tames the atom with three simple rules. Compute hydrogen energy levels and transition energies for the spectral lines.
Rutherford's modelMost of the atom is empty space with a tiny, dense, positively-charged nucleus; electrons orbit around it (from the gold-foil experiment).
Bohr's postulatesElectrons orbit only in fixed "stationary" orbits (angular momentum = nh/2π) without radiating; they emit/absorb a photon only when jumping between orbits.
Energy levels of hydrogenThe allowed energies are Eₙ = −13.6/n² eV. The negative sign means the electron is bound; n = 1 is the ground state.
Spectral seriesTransitions to n = 1 give the Lyman series (UV), to n = 2 the Balmer series (visible), to n = 3 the Paschen series (IR).
Hydrogen energy-level calculator Interactive
Enter the orbit number n to get the energy and radius of that level in a hydrogen atom.
Energy, Eₙ = −13.6/n²—eV
Radius, 0.529·n²—Å
Higher orbits are larger and less tightly bound (energy closer to zero); n = ∞ means the electron is free (E = 0).
Numericals practice Interactive
Energy-level and transition problems with steps.
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Solved numericals
Q2. What is the ionization energy of a hydrogen atom in its ground state?
Ground state energy E₁ = −13.6 eV
Ionization means moving the electron to n = ∞ (E = 0)
Ionization energy = 0 − (−13.6) = 13.6 eV
Formula sheet
| Quantity | Formula | SI unit |
|---|---|---|
| Radius of nth orbit | rₙ = 0.529 n² Å | ångström |
| Energy of nth orbit | Eₙ = −13.6 / n² | eV |
| Transition energy | ΔE = 13.6 (1/n₁² − 1/n₂²) | eV |
| Angular momentum (Bohr) | L = n h / 2π | J·s |
Common mistakes & exam wins
- Energy Eₙ = −13.6/n² is NEGATIVE because the electron is bound to the nucleus.
- Balmer series (jumps to n = 2) lies in the visible region — the lines you actually see.
- The ground state (n = 1) is the most stable and most tightly bound.
- Ionization energy of hydrogen = 13.6 eV (energy to remove the electron from n = 1).
Frequently asked questions
What are Bohr's postulates?
Electrons revolve in fixed stationary orbits (with angular momentum nh/2π) without radiating energy, and emit or absorb a photon only when jumping between orbits.
What is the energy of the nth orbit of hydrogen?
Eₙ = −13.6/n² eV; the negative sign shows the electron is bound, and n = 1 is the lowest (ground) state.
What is the Balmer series?
The set of spectral lines emitted when electrons fall to the n = 2 level of hydrogen; these lie in the visible region.
What was the conclusion of the Rutherford gold-foil experiment?
That the atom is mostly empty space with a tiny, dense, positively charged nucleus at its centre.