2aAtomic Models and Bohr's Model
Trace the evolution of atomic models from Thomson to Rutherford to Bohr, and master the quantized energy levels of hydrogen.
The Bohr model was the first successful quantum model of the atom — it correctly predicted hydrogen's spectral lines and introduced the concept of quantized energy levels that underlies all of modern chemistry and atomic physics.
Lesson Overview
Our understanding of the atom evolved through a series of models. Thomson's plum-pudding model (1904) placed electrons embedded in a positive sphere. Rutherford's gold foil experiment (1911) revealed a tiny, dense, positive nucleus. Bohr's model (1913) combined classical orbits with quantum rules: electrons occupy only specific allowed orbits with quantized angular momentum, and emit or absorb photons only when jumping between orbits. For hydrogen, the energy levels are Eₙ = −13.6/n² eV. While the Bohr model was eventually superseded by quantum mechanics, it correctly predicts hydrogen's spectral lines.
Key Concepts
Thomson Model
Plum-pudding: electrons embedded in a diffuse positive sphere (1904)
Rutherford Model
Nuclear model: tiny dense positive nucleus, electrons orbit outside (1911)
Bohr Postulates
Electrons in fixed orbits; only certain radii allowed; photon emitted/absorbed on transition
Hydrogen Energy Levels
Eₙ = −13.6/n² eV (n = 1, 2, 3, …); ground state n=1 at −13.6 eV
Bohr Radius
Smallest allowed orbit: a₀ = 5.29×10⁻¹¹ m; rₙ = n²a₀
Limitations of Bohr Model
Only works for hydrogen; cannot explain multi-electron atoms or fine structure
Calculate the energy of the hydrogen atom in the n = 3 energy level.
A hydrogen electron transitions from n = 4 to n = 2. Calculate the energy of the photon emitted.
Describe Rutherford's gold foil experiment and explain what result was expected vs. what was observed.
What is the radius of the n = 3 orbit in hydrogen? (a₀ = 5.29×10⁻¹¹ m)
What is the ionization energy of hydrogen from the ground state? What does ionization mean?
Calculate the energy of the hydrogen atom in the n = 5 level and find the energy needed to excite it from n = 1 to n = 5.
Hint: Use Eₙ = −13.6/n² eV. The excitation energy = E₅ − E₁.
A photon of energy 10.2 eV is absorbed by a hydrogen atom in the ground state. To which energy level does the electron jump?
Hint: Find n such that Eₙ = E₁ + 10.2 eV = −13.6 + 10.2 = −3.4 eV. Solve −13.6/n² = −3.4.
Why did the Rutherford model of the atom have a fatal flaw according to classical electromagnetism?
Hint: A charged particle moving in a circle accelerates. What does classical EM theory say about accelerating charges?
Calculate the radius of the n = 2 orbit in hydrogen and compare it to the ground state radius.
Hint: Use rₙ = n²a₀. How does r₂ compare to r₁?
List two phenomena that the Bohr model successfully explains and two that it cannot explain.
Hint: Think about what the Bohr model was designed for (hydrogen spectra) and where it breaks down (multi-electron atoms, fine structure).
Key Vocabulary
Rutherford Model
The nuclear model of the atom: a tiny, dense, positively charged nucleus surrounded by electrons orbiting at relatively large distances.
Example: Rutherford's gold foil experiment showed that most of an atom is empty space, with mass concentrated in a nucleus ~10⁻¹⁵ m across.
Bohr Model
A quantum model of the hydrogen atom where electrons occupy only specific allowed circular orbits with quantized angular momentum.
Example: In the Bohr model, the hydrogen ground state has energy −13.6 eV and radius 5.29×10⁻¹¹ m.
Energy Level
A discrete, allowed energy state for an electron in an atom. For hydrogen: Eₙ = −13.6/n² eV.
Example: The n=2 level of hydrogen has energy −3.4 eV; the n=3 level has −1.51 eV.
Ionization Energy
The minimum energy required to completely remove an electron from an atom in its ground state.
Example: Hydrogen's ionization energy is 13.6 eV — the energy needed to remove the electron from n=1 to n=∞.
Interactive Practice — 5 Questions
Rutherford's gold foil experiment showed that:
In the Bohr model, the energy of hydrogen's n=2 level is:
When an electron in hydrogen jumps from n=3 to n=1, the atom:
The ionization energy of hydrogen from the ground state is:
A major limitation of the Bohr model is that it:
Independent Practice
List the three atomic models (Thomson, Rutherford, Bohr) in chronological order. For each, describe the key experimental evidence that supported or refuted it.
Calculate the energies of the first four hydrogen energy levels (n = 1, 2, 3, 4) in eV. Draw an energy level diagram.
A hydrogen electron transitions from n = 5 to n = 2. Calculate the photon energy emitted and determine whether it is in the UV, visible, or IR range.
Explain why the Rutherford model predicted that atoms should be unstable (electrons should spiral into the nucleus) and how Bohr's postulates resolved this problem.
★ Calculate the wavelength of the photon emitted when a hydrogen electron transitions from n = 3 to n = 2 (the H-alpha line). Compare your answer to the observed value of 656 nm.
ChallengeCommon Mistakes
Thinking higher n means lower energy (more negative).
Higher n means higher (less negative) energy. n=1 is the lowest energy (most negative, −13.6 eV); n=∞ is 0 eV (free electron).
Confusing emission (electron drops to lower n) with absorption (electron jumps to higher n).
Emission: electron falls to lower level → photon released. Absorption: photon absorbed → electron jumps to higher level. Photon energy = |ΔE| in both cases.
Math Tips
For hydrogen energy levels: Eₙ = −13.6/n² eV. Photon energy for a transition: E_photon = |E_upper − E_lower| = 13.6(1/n_lower² − 1/n_upper²) eV. Always take the absolute value — photon energy is positive.