Read Bohr's model as three explicit postulates, not as a single formula. First, the electron may occupy special stationary states without radiating. Second, the allowed circular orbits satisfy \(L=mvr=n\hbar\). Third, radiation is emitted or absorbed only when the electron jumps between two allowed states, with \(hf=\Delta E\).
After those rules are stated, classical mechanics enters as a calculator: Coulomb attraction supplies the circular force balance and the mechanical energy, while the postulates select which radii, energies and spectral frequencies are allowed.
Bohr keeps the planetary picture of an electron orbiting the nucleus, but changes the rules that decide which orbits and transitions are physically allowed. The model is deliberately hybrid: classical circular motion plus quantum restrictions.
The postulates should be read separately, because each one repairs a different classical problem.
- Stationary states: the electron can occupy certain circular orbits without continuously radiating energy.
- Angular-momentum quantization: only orbits satisfying \(L=mvr=n\hbar\) are allowed.
- Quantum jumps: light is emitted or absorbed only when the electron moves between two allowed states.
The first equation selects the allowed orbits. The second equation connects a spectral line to the energy difference between two stationary states.
The model therefore turns a color into a level difference: measuring \(\lambda\) gives \(hf=hc/\lambda\), and that equals \(\Delta E\).
The electron is still treated as moving in a circular Coulomb orbit. The inward electric force supplies the centripetal force:
Using the force balance in the energy expression gives \(E=-\kappa e^2/(2r)\). Quantization then restricts which radii, and therefore which energies, are possible.
Exercises on the Bohr model usually ask which postulate is doing the work. The first postulate says that stationary states exist and do not radiate while the electron remains in them. The second postulate selects the allowed states through angular momentum quantization:
The third postulate connects transitions between stationary states with emitted or absorbed radiation:
Keeping these roles separate prevents a common mistake: the model does not explain radiation from a classical accelerating charge; it replaces that picture with quantum jumps between allowed energies.
This page is designed to support short guided exercises on: Stationary states, angular momentum quantization and quantum jumps in the early atomic model.
- Use from this page: the definitions, physical setup, highlighted equations and conceptual links needed to start a first calculation or explanation.
- Keep in the book: complete derivations, extended historical discussion, worked solutions and the full textbook narrative remain in the original chapter and linked book resources.
- Good exercise balance: ask the student to identify assumptions, apply one relation, and interpret the result physically, without requiring material not introduced on this page.
Use these anchors to design compact exercises. The exercise should be answerable from this page plus standard algebra, while longer derivations, full worked examples and broader context should point back to the original book.
- Focus: Stationary states, angular momentum quantization and quantum jumps in the early atomic model.
- Conceptual check: state what the main result says physically before using it algebraically.
- Equation: \[L=mvr=n\hbar\]
- Equation: \[hf=\Delta E=E_i-E_f\]
- Equation: \[E=\frac{1}{2}mv^2-\frac{\kappa e^2}{r}\]
- Boundary: use this page for setup and first-step reasoning; cite the book for longer derivations, complete experimental history or solved-problem detail.
- Typical task: derive, interpret, or apply the relation above to a simple case without introducing topics outside this page.